A good gallery is booked, generally for a year or more.
Keep in mind that serious galleries receive thousand of books every week, they of course never check them.
The very best galleries will contact you, not the other way. How? because they know who you are and at one point they want you.
It means that you have to be in the circuit for some time in much more humble spaces, generally starting with collectives.
You make yourself a name and a reputation step by step. Reasonably think about 9-10 years to reach that.
If you are really good*, a serious gallerie might contact you.
*really good here means that a gallerie is a business institution and therefore do not expect fairness. They want to sell and make money. If the gallerie is good you will make a lot of money too.
Social contacts are a part but only a part. I know very famous photographers in a genre with impressive contact list that have hard time to enter a serious art gallery.
There is a legend on that. They have hard time despite they relations simply because the gallerie has a clientèle focused in a certain style and if you do not belong
to their customer's demand, relations or not, you will not enter. The commercial circuit is not the same at all from the art one. There is almost no bridges.
Nobody can't enter this
gallerie in Madrid for example, even if your relations are enormous, even if you get married to the lady in charge. If your name is Robert Longo you will have a welcome place even if you are an unbearable person to deal with.
Sometimes, if a young* artist (in fine arts for example) is really good, teachers inform the galleries that there is a promissed "star". They keep an eye on the person, how she-he grows.
*young in art does not specially mean young in age. You can be 50 and being young in the circuit.
It is exactly like formula 1 car race. You don't enter a F1 team, they call you when they estimate you will make them earn a lot of money and prestige.
Start from the bottom in collectives with zero expectations. Do not target the big ones even if you estimate that your work is good. They have to estimate that (not the artist) based on their own criterias. If you call a big gallery not being "ready", you gain a bad reputation and it is even harder to come back later. Just exhibit where you can.