One very good thing here is that your gf didn’t get injured when this happened. A blown front tire can easily cause the car to become uncontrollable. So count your blessings that the only problem is a blown tire and a tie rod on the fritz.
As far as the shop’s culpability, I’m with the others. They wouldn’t have knowingly let the car be driven away if they knew the tie rod was about to snap. They may have missed the problem, or the problem was an invisible crack at the time. But either way, there’s no evidence I can see pointing to it being a problem with the shop.
“If you could successfully sue for what if’s, we’d all be filthy rich…”
Exactly
In order to win a civil suit, you have to prove that you suffered specific damages.
A hypothetical “it could have happened” claim would not win a case for you.
I don’t see how the OP thinks they can legally sue or take any kind of legal action at all on a car that belongs to the girlfriend unless the OP has their name on the title as “and/or”…