Following on with a comment and one possible real answer. First, you didn't say whether this was for a dedicated configuration (e.g., only runs the browser) or a general purpose case, where you simply care about how fast the browser starts. I assumed a dedicated configuration, based on your description. This answer addresses the dedicated configuration.
First, install a minimal X11 configuration and browser: sudo apt install xserver-xorg xserver-xorg-core xserver-common icewm icewm-themes xterm x11-apps xfonts-base xfonts-100dpi xfonts-75dpi xfonts-scalable chromium-browser firefox-esr
I'm suggesting that you use icewm for a window manager because it's lightweight and configurable. There are several good window managers, so feel free to use a different one.
Next, in your login directory (e.g., /home/pi for the pi user):
mkdir .icewm
cd .icewm
echo "ShowTaskBar=0" > preferences
echo "#!/bin/bash" > startup
echo "firefox & " >> startup # Change the browser command as desired
chmod 755 startup
To get it all started, type startx after you login.
If you'd rather no use a window manager at all, you can create the file ~/.xinitrc with the contents exec firefox (or other browser). This will start the X11 server running the browser (and nothing else).
Of course, you may want to have the graphical environment come up automtically when you start the system. If that's the case, there's a bit more to do. Please clarify the completely problem you're trying to solve.
