How to find a job without recommendation letters?
The situation is difficult so the solution may also be difficult. I can offer only a few suggestions.
If you are just four years past finishing your doctorate it isn't too late to re-connect with your previous professors, and maybe your advisor. If you wait much longer it will be, however. The best way is to visit your old institution in person and spend a couple of days talking to people and reminding them of who you are. You can also talk to them about research ideas - theirs and yours. But you can also let them know why you have been away and that you'd like to get back into academia. If you were once well regarded then you still are, but they need a reminder. Such a visit might be the best "vacation" you've ever had.
Another thing, not very palatable, is to get some low-level position in a decent university where you can do more than is required by the job. If you can let the tenured faculty know of your skills and interest, maybe you can be given interesting tasks that will lead, after a while, to good letters of recommendation. It may not be possible to work up from a low level position to a better one at that university, but you may be able to leverage it for a position somewhere else.
Further down the list of suitable options is to look at good secondary institutions, rather than universities. There are many of them that find people with doctorates to be very desirable. The job is mostly teaching, and mostly introductory subjects, but it can pay the bills. If the place is also located close to a good university, you can make yourself known there and try to get connected to a research group so as to get some papers into publication. Initially they might be joint papers, of course.
But don't let your age be a deterrent. You will get older no matter what you do. Many people don't start their career until your age, in fact. But take a long view into following whatever opportunities present themselves, always with a view to a higher level position.
Can someone please help me in right direction of finding an academic or non-academic job? Minimum salary will be acceptable.
If you really are just looking for anything at all to bring in a little bit of money to get back on your feet, I'd suggest looking for work as a tutor. You don't even necessarily need to apply for this job. In many cities I've seen freelance tutors advertising their services on paper flyers on noticeboards in cafes or shops, or you can post on local message boards like NextDoor or Craigslist. Look at ads for other tutors for inspiration. With your academic credentials and teaching experience, you could charge a fairly high hourly rate.
If you prefer a more structured environment, you could apply to be a tutor at a large tutoring company like Kaplan. They will not require academic recommendation letters, but they may ask you to demonstrate your competency at standardized tests.
Somebody else had suggested teaching at a secondary school, and you mentioned the lack of teaching credentials as an obstacle. Depending on what country you're in, private schools may not require any official teaching certification, and they may be happy to employ an instructor with a PhD because it will make them seem prestigious.
You mention that you are German citizen. A few thoughts that are rather specific to Germany (assuming that is where you are as well):
In Germany, Arbeitszeugnisse are [still] more usual than letters of recommendation, even though for academic positions letters of recommendation will be accepted in lieu. The Arbeitszeugnis is a letter by the employer certifying what the employee did and how they performed. At/after the end of an employment contract, the employee has a right to get one of these, and it must be both truthful and reasonably positive.
If you were previously employed in Germany, it may still be possible to get one. As is is a legal right, the employer cannot turn down the request unless they gave you one already when you finished there.almost homeless
Time to talk to the Sozialamt at your community center/town hall. That's probably not going to be fun, but it may be crucial.
Also organizations like Diakonie or Caritas or if you prefer one without Christian affiliation, the Arbeiterwohlfahrt may help you by having people who know how to talk/write to the Sozialamt (I don't know whether other religious communities have similar organizations, they may, or they may also have similar help organized on a more informal basis).
These organizations also offer postal addresses in case you do become homeless - the postal address is crucial in order to get a job.Mathematics teachers at school are scarce in all Länder. Some Länder offer training programmes for professionals in certain subjects (including STEM) who did not do the university courses to become a teacher.
This will obviously require excellent command of German, written as well as spoken.If you look for possiblities to get back to academia, consider also Fachhochschulen (universities of applied science) if you can land an industry job. In contrast to universities, Fachhochschulen want industry experience.
Germany has lots of small to medium-sized companies, and also quite a number of universities outside the big cities in rural areas. The rumor has it that they have difficulties finding people - this may be your chance, at the very least as a (re)entry into the job market.
I'd roughly say: the larger the company/university where you apply, the less likely I expect them to be willing to overlook your difficulty in producing recommendations.
And in contrast to many other regions world-wide, rural Germany has IMHO a very acceptable living standard almost everywhere (and maybe a much better wage : living expenses ratio).You can tutor students and pupils. Mathematics is quite in demand in that respect.
In order to do so legally, you'll need to sign up as freelancer with the tax office and with the pension cass (while freelancers in general are not required to contribute to the governmental pension cass, freelancing teachers are unless they have employees). This option has burocratic consequences such as being required to do tax declarations and earlier deadlines for these tax declarations. Ask e.g. the local IHK what (free) information is available for possible founding of such a small scale business. The IHK is not exactly for freelancers, but they'll know about courses (free and paid).
Since you are mathematician, the DMV may be helpful (i.e. I'm chemist, and the GDCh has a tiny but helpful subsection for freelancing chemists and people who think about becoming freelancers in chemistry).Still thinking in direction of teaching: I have no idea whether something like being a certified instructor with the carpentries helps (that's where I volounteer). The course has certainly helped my teaching, and it may show that you are serious in wanting to become a teacher. Also, if you volounteer with them (which costs you time, and you'll have to be able to pay upfront for the travel until the reimbursement arrives) you're going to meet different univeristies/institutes in person, and moreover they'll see you working. It may be worth while thinking whether such opportunities could get you over the lack of recommendation obstacle. That is also a community where related jobs (worldwide) are reqularly posted on their mailing lists. Of course you can sign up for the mailing list without being an instructior, but I'd expect your chances there are much better if you are known in the community.