Get a timestamp from concatenating day and time columns

date and time types

If your Day is of type date and your Time is of type time, there is a very simple solution:

SELECT EXTRACT(EPOCH FROM (day + time));

You can just add date and time to get a timestamp [without time zone] (which is interpreted according to the time zone setting of your session).

And, strictly speaking, extracting the epoch is unrelated to your question per se.
date + time result in a timestamp, that's it.

String types

If you are talking about string literals or text / varchar columns, use:

SELECT EXTRACT(EPOCH FROM ('2013-07-18' || ' ' || '21:52:12')::timestamp);

or

SELECT EXTRACT(EPOCH FROM cast('2013-07-18' ||' '|| '21:52:12' AS timestamp));

Your form does not work

SELECT EXTRACT(EPOCH FROM TIMESTAMP ('2013-07-18' || ' ' || '21:52:12'));

This would work:

SELECT EXTRACT(EPOCH FROM "timestamp" ('2013-07-18' || ' ' || '21:52:12'));

I quote the manual about type casts:

It is also possible to specify a type cast using a function-like syntax:

typename ( expression )

However, this only works for types whose names are also valid as function names. For example, double precision cannot be used this way, but the equivalent float8 can. Also, the names interval, time, and timestamp can only be used in this fashion if they are double-quoted, because of syntactic conflicts. Therefore, the use of the function-like cast syntax leads to inconsistencies and should probably be avoided.

Bold emphasis mine.
The gist of it: rather use one of the first two syntax variants.

SELECT EXTRACT(EPOCH FROM (Day || ' ' || Time)::timestamp);

This works fine for me :

SELECT CONCAT(Day,' ',Time)::timestamp;