> if every nation worked together with NASA to start exploring and evaluating our solar system planets
You mean like the way that NASA works with ESA and with JAXA?[1]
Oh, and it isn't up to other the other nations - if NASA wants to work with another agency, it is up to NASA to ask (and vice versa).
> and then start looking at others in our Galaxy
You do know that we have been looking at other stars and planetary systems in our galaxy for a while now? Little things like the JWST - although, as far as the stars go, NASA is way behind the curve, people all over the world have been looking at those for, oooh, years - a good few thousand if them at least, going by recorded observations.
> NASA is far more likely to get it done if everyone in the world was working together.
NASA is not the be-all and end-all of "looking at other stars and planetary systems"; actually, they do very little of the looking, but do do more of the sending robots for some very specific little bits of in-situ work.
[1] and others, but you could try googling for those yourself