Before you open your gallery, you should carefully assess all the risks. Basically, this is the same business as, for example, opening a store so you will need a business plan. Your strategy must be thoughtful and clear, so as not to fall into a debt hole later or be left with nothing.
If you are confident in your decision, there are several ways to get funding.
Art is an important part of our life. In addition, it can be said that it is fashionable in the circles of businessmen and all those who have a lot of money. So rich people sometimes don't mind investing in a new gallery or up-and-coming artist. So there is a chance to get the necessary funds without returning them.
Investors are the same rich people but do not want to part with money just like that. Investors can offer you the necessary funds with the conditions for their return. It can be a one-time payment or a percentage of the profit after a certain period.
In America, many foundations support the arts. You can submit several applications to various funds and possibly, receive a grant. It may not cover all expenses, but it can help a significant part. It all depends on the fund you choose and the amount of the grant you will receive.
After all, you can always take out a loan. Of course, this requires a good credit score and income to borrow a huge amount of money at reasonable interest rates. Or be the owner of a house that can be used as collateral. True, if things go badly, you can lose your home, but who does not take risks does not have his own gallery.