Well, this is interesting. The OP gave us 3 sentences, and only one of them is relevant, but we are all engaged in various interpretations of what he/she is asking. It's quite likely the OP doesn't even realize the possibilities this question opens up.
The Linux Mint installer on LM20 MATE Edition (Ubiquity) does not have the Try/Install option that is shown with Ubuntu (it has an OEM install for manufacturers, but that is different). So the Mint bootloader takes us to a desktop, and there is an icon there to run the installer. Maybe other Mint editions have Try/Install, but I just booted on MATE, and it doesn't.
The OP asks about leaving a "base system of Mint 20" after removing the installer. For my part, I do NOT consider a "live system" to be the same as a "base system," though perhaps that is indeed what the OP wants. A "live system" boots up without a login (with Mint, but not all distros), and it has full root privileges. That's fine for an installer that needs root (and to test hardware compatibility), but it's not typical in a "base Linux system." It goes against our lifelong Linux lesson: don't use root unless you need it.
Even a "live system" with persistence is not a "base system" (IMO) due to limitations with this method, such as being difficult or impossible to upgrade the kernel or install drivers (see here
). Maybe there are workarounds even for this these days. Maybe, for the OP, using Mint with persistence and deleting the desktop installer icon would be good enough. Maybe we are all over-thinking the question.