Using a 12 V 3 A bilge pump on a 12 V 8.5 A LED power supply

Most certainly a surge (or in-rush) current problem. Electric motors, at start-up (when they are not spinning yet) and especially when driving a load (like turning the pump's impeller against water) draw enormous short-term (surge) current. This surge quickly dies out once the motor "gets going".

From wikipedia

When an electric motor, AC or DC, is first energized, the rotor is not moving, and a current equivalent to the stalled current will flow, reducing as the motor picks up speed and develops a back EMF to oppose the supply. AC induction motors behave as transformers with a shorted secondary until the rotor begins to move, while brushed motors present essentially the winding resistance. The duration of the starting transient is less if the mechanical load on the motor is relieved until it has picked up speed.

You have just come face-to-face with a fact of life: the starting current for a motor is much larger than the running current.

For DC motors the rule of thumb is the starting current is about 3 times the running current. So a 12.5 amp supply should be adequate for a 3 amp motor. But.

1) The current rating for the bilge pump may or may not reflect the added power required to pump water, rather than just spin the rotor.

2) A cheap Chinese power supply may or may not live up to its specifications.

So, a couple of steps to take:

Get a decent meter, and measure the resistance of your bilge pump. It's probably about 1 ohm with the rotor not moving. Be careful to compensate for the resistance of your meter probes. When you first apply power, the current needed will be 12 volts divided by the resistance. As the pump starts turning, it will internally produce what is called back EMF which will effectively reduce the voltage and therefor the current - but you must apply the full current long enough to get the thing spinning.

Get a power resistor of the same resistance as the motor, and something like 100 watts. Connect this to your 12.5 A supply, turn on the juice and measure the voltage. If the voltage stays up at 12 volts, you know the supply is up to spec. If the output voltage falls, you know you've been had. It may or may not be a bad unit.

An LED power supply isn't meant to power inductive loads like pumps.

Now, an 8.5 A supply should be sufficiently oversized to drive a 3A motor, but honestly: I believe neither the rating on amazon-bought power supplies nor on bilge pumps, so that leaves it up to you to figure out (e.g. by actually measuring the current) to figure up who's wrong.