There's the legal requirements to run for Congress and then there's the realistic requirements to run for Congress, in my opinion. Yes, a 25 year old American citizen can run for the House of Representatives, but he or she would have to be extraordinarily mature in order to win election. It's been my experience that most successful candidates for the House have already held a local public office and are at least in their early 30s.
The other reality is that the political parties, both Republican and Democrat, are only going to back a candidate who looks electable. Without that financial and political support behind him or her, a person's chances of winning an election are minimal. Someone without major party backing might win a few sympathy votes or some votes against the main candidate, but that's about all.