The road to victory is very narrow here which explains why there aren't that many general considerations which will hand you the win. You really need to find most moves by visualization. Except perhaps the first move bxc6+ which you would play because it opens up attacking lines to the black king. The second move is one of sheer desperation unless you also calculated that you could capture the rook and survive black's counter attack which requires even more precise calculations. It is simply a hard tactic even for players of >2000 rating.
Note that white would draw at best with an extra white pawn on c2! That tells you how evaluations may depend on seemingly insignificant details. But not all is hopeless. Like the modern engines your body has its own neural network that feeds your chess intuition. Most likely it sends you the message that a position like this one should be winnable - the result of many years of playing chess. And it will encourage you to continue visualizing until you find a way. And when you are strong and experienced enough, you will indeed find that way and win the game. Neural networks are a bit like magic!
I was doing tactics training, and I came across this puzzle. First of all, to get good at tactics, do we really need to be able to calculate puzzles like this where there are 10 different variations, 8 moves in the future?
Nonetheless, after 3.. Bb5, is there some trick to calculating all the possible forks, so that way you wouldn't lose the game in real life (to prevent Qxf1)?