Yes Digikey are expensive and is there for professionals, who's time is so costly, it works out cheaper than faffing around searching for it elsewhere and waiting for it to turn up.
There are some parts which are inherently costly. After the transformer, there are the capacitors, which need to be good. You can try your luck on Amazon and ebay but you can never be certain they're any good. The key features you need are low ESR and high ripple current rating.
If you want a challenging project, then you could build a 12V 50A switched mode power supply, but it's not a beginner friendly project because it involves capacitors charged to mains voltages and having to design transformers and a PCB with adequate insulation from the mains. You'll probably also need to get yourself a massive isolation transformer for test purposes.
Yeah I'm not going to do that. People seem to have a disconnect between what is ideal and what is practical. They often tell you to buy the best test equipment for some thing you are going to do once or recommend things that a beginner would try but then get frustrated and give up once they realize its way too expensive and learning how to do it would put you half way to a BS in EE. Its like running a business, there is a middle ground of practicality and isn't found in any text book but comes from common sense. Often great engineers are shitty business people because they can't step back and say "Yes I would do that, but when I was just starting or an average mechanically inclined person would it make sense to do that if it was even possible?" Sometime the quick and dirty solution is the best solution when all that matters is the outcome and not how you got there. But conversely when the outcome isn't as important (its not to make a financial gain or just get something working) what is of value is learning from the process. No one blinks an LED on off because their house needs strobe lighting or they own a blinking led company its to learn how it works, even if it doesn't work hopefully they learned what not to do.
Sorry, I don't see the point, you're trying to make?
In this case the most idea/practical solution is to buy a suitable switched mode power supply, for your amplifier. I agree that designing one is not feasible for a beginner.
There isn't much you will learn by building a PSU, using a huge transformer, rectifier and capacitor. It would just be the same small power supply just scaled up. It's also inferior to using a switched mode power supply, in just about every single way. Quite often people avoid switched mode power supplied for audio applications, but in this case, it's a car amplifier, which will have plenty of filtering and a switched mode power supply built-in, to increase the voltage to a level, to deliver the required power into an 8 or 4 Ohm speaker.
A good pen and paper exercise would be reverse engineering the existing amplifier and performing some tests on it, to check if it really meets its advertised specification. Quite often manufacturers grossly exaggerate the specifications for their audio amplifiers and it would be interesting to see whether this is the case here.