So you have a known good motor and a known good installation environment
So you have a known good motor and a known good installation environment. The work to ensure both of these conditions caused some delay but prevented failures that result from a rushed motor swap. But don't unwire and yank the old motor just yet. You need to continue down your motor replacement checklist.
That checklist should have you ensuring lockout/tagout and not just of electrical sources. For example, if the motor operates a large press, then you need to block the press to eliminate any chance of mechanical operation (such as by gravity). While this is going on, someone needs to conduct "as-installed" insulation resistance tests on the replacement motor for baseline data. Someone else needs to obtain the torque specs for the mounting hardware (which should all be new), plus a torque wrench suitable to the job.
Once you have isolated the energy sources, your next checklist step is to note how the old motor is mounted, wired, and connected to the load. Note the orientation and condition of any vibration isolators. Before lowering the new motor into place, ensure fingers and tools are out of the way. Shim the motor to level it, but don't fully torque the fasteners until after you've aligned the motor.