Asking how would you prove is making the assumption that there already are and that isn't the perspective science takes to discovery.
There is a very high likelyhood of life elsewhere in the universe and we will continue to send rovers and probes to planets that have a similar composition as Earth to collect data, analyze it, and bring it back when possible.
A million dollars doesn't really mean much. Fundamentally, it's a pile of cellulose and cotton. It takes research effort and luck to make discovery happen. If you gave a scientist today 1000000 trillion dollars to discover life on other planets, it won't mean a thing. They'd still have to think and guess and the limits of our brain can't be overcomed simply by having a lot of money. On the other hand, there can now be MORE research because there's funding for projects but when it comes to research, 100 million dollars doesn't make much progress.