Welcome to the community @Donna Austin ! The way I usually handle this is by adding the trello chrome extension, and when i want to go to a specific board, i just go to my URL and type "t" then tab, and i can search the name of the board I want. You could also use bookmarks, although it sounds like that's what you're trying to avoid.
You can set Chrome to load certain pages anytime a new tab is opened, or anytime a new window is opened, at which point maybe that behavior would create a "default" tab directing to the board you want?
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