Sounds like you want the browser to open to a homepage aka “New Tab Page” of your choice.
When the mobile browser starts, by default/design, it displays a homescreen aka “New Tab Page” aka “NTP”.
Some users want to choose a background scene replacement for that NTP.
If your mobile device’s Brave Browser is - upon startup - displaying a NTP, you can add a website widget tile to that display (and you can remove widget tiles):
Settings > New Tab Page > WIDGETS > [Enable] Favorites
For example, by default, after a fresh install of the mobile Brave Browser, the NTP dislays a handful of webpage widget tiles. IIRC, for:
Facebook.com
X.com
Yahoo.com
- a few others
I prefer a clean NTP and remove all those widget tiles.
But, if I were to pick one webpage widget tile to have, I would Enable that Favorites setting, visit the webpage-of-choice, and then click the Share button.
In the resulting window, select “Add to Favorites”
That would place a widget tile icon representing the website, onto the NTP.
When starting up Brave Browser, I would click that widget tile.
Apologies where I may not have the terminology precisely correct; and, I am using my iPhone displays and settings info for reference (IOW, not an Android OS).