You won't get hired on a "temporary visa."
Without a clear right to work you may not, uh, work in the US. It's the same as if I wanted to be an airline pilot in the UK.
Green cards are (unfortunately) much more of a lottery system than merit-based. The two "easiest" options are 1) invest $800,000 in a US business or 2) get married, legitimately, to an American.
There are flight schools in the US where you can have the stated educational goal of ATP. ATP requires 1,500 hours. The normal way to get there is through instructing. So, the visa lets you instruct from Commercial/CFI to 1,500. And get paid. This can easily take three years. If you are a decent guy w/ a few quid you'd stand a good chance of meeting someone you might want to marry.
But please marry for love, not for a green card!
Alternatively, move to Australia and become a citizen. Australian pilots may get visas to fly in the US.