Yes, you can build a bootable macOS USB stick; you'll need at least an 8Gb stick.
It'd help if you mentioned what model of Mac Mini you have, and the CPU type: this will dictate the most recent version of macOS that it can run, hence the procedure for building the bootable USB stick. Or, if you can find an external SuperDrive (Apple DVD-RW) you can boot off that — but not a regular external USB DVD drive, alas.
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Date: 2018-10-29 10:31 am (UTC)It'd help if you mentioned what model of Mac Mini you have, and the CPU type: this will dictate the most recent version of macOS that it can run, hence the procedure for building the bootable USB stick. Or, if you can find an external SuperDrive (Apple DVD-RW) you can boot off that — but not a regular external USB DVD drive, alas.