Can algorithm discovery be brute forced?
You are correct in saying that algorithms are no more than a sequence of strings. However, you should make the distinction between syntactic and semantic properties of the algorithm. Syntactic properties are those relating to the actual code, e.g. what is the length of the program? how many "while" loops does it contain? Semantic properties are related to what the program actually does, e.g. is there some input that would cause this program to go into an infinite loop?

The problem you encounter in your suggestion is that almost every interesting semantic property is undecidable, meaning that even with unlimited resources (time/memory) you cannot algorithmically reason about this property just by looking at the source code.
So in fact, the situation is worse than what you think. Even the craziest hardware won't help us, since such tasks are impossible for a computer.

As a side note, suppose your situation was better, and you try to cope with some decidable problem which has an exponential lower bound (i.e. all algorithms for this problem would require exponential time, not just brute force search, even the "smart" ones). Again, better hardware won't help you. For some intuition regarding your parameters, you have $\approx 10^{80}$ atoms in the universe, so performing this amount of operations is hopeless. What you need is a smarter algorithm, but we started with a problem that unfortunately has an exponential lower bound.