Your post is a little difficult to follow as in, where exactly are you trying to get to and from?
You are correct that the furthest south the BART runs is SFO, but the Cal-Train goes all the way past San Jose and stops in Santa Clara and the San Jose airport.
Uber would be extremely expensive from SF to Santa Clara. If you aren't staying in The South Bay I'm not sure why you would fly into and out of San Jose though. If you plan on staying in SF and attending games in Santa Clara, fly into SFO, stay in SF and take the train to Santa Clara. I'm not sure how it will operate for Copa but during 49er games the train is a booze cruise and you're allowed to drink on the way down. (like they would ever stop it anyway)
I'm thinking about flying in to San Jose on Friday, go to the U.S. match, probably spend the night in a hotel near Santa Clara. On Saturday, head into San Fran for the weekend. Spend Sat and Sunday in the city and then head back south Monday afternoon for the Argentina match. Spend the night in Santa Clara/San Jose Monday night and fly out of San Jose on Tuesday. I was just curious what options there were to get to SF from the South Bay Area. I was unaware of the Cal-Train option so thanks for the heads up on that.