It's kind of odd that you have no output tube specs in your "thought experiment" but I will play along.
I guess we assume that the amp is wired correctly and that tubes are in serviceable condition. (Don't laugh; I once worked in an electronics factory fixing stuff right off the ass'y line after it failed the first "power on" test, and under those conditions, you have no right to assume that the device *ever* worked properly)
You would probably start by looking at the tubes and comparing them to known types. If they appeared to be beam power tubes or tetrodes, I would look to see the voltage ratings of the p/s caps. I would examine the circuitry and see if it's something resembling a push-pull output (you did say tubeS plural)
I'd insert 1 ohm resistors in the cathode circuits of the output tubes.
Assuming all that achieves a picture of a generally typical push-pull output section, and again, we are assuming the amp once worked and has not been randomly rewired, thus there is some sort of bias circuit there) Maybe it is fixed, maybe is variable. At some point, I guess I would have the confidence to power up the amp, hopefully there is a standby, and I'd set the bias to a very high (negative, of course) voltage to where I'd be pretty sure the output tubes would be shut off. Turn on B+. Await smoke. Or, if the bias was fixed but I had no confidence that the output tubes wouldn't overcurrent, I would have to build a simple bias supply and hotwire it into the circuit such that I could turn on B+ and be quite sure that the output tubes wouldn't fry. Give 'em -100 volts or so negative bias.
And basically, feed the amp a sine wave of an amplitude typical of how the amp would be used, and crank down the negative bias (eg; make it more positive, closer to zero, output section more and more turned on) while looking at the output on a scope and monitoring cathode current. At some point, the thing starts to amplify...or not...but assuming that I eventually get some kind of signal on my output, I would turn on the output section more and more until the cathode current (if the tube was the size of a 6V6) landed into 6V6 zone, or if larger, then larger. Run it for a while into a dummy load, check in to see if anything was burning or smelling funny.
If I was looking for tweed-style breakup, I might be looking for one thing. If I wanted "high-fidelity" I'd be sensitive to when distortion started showing up (which you can barely see on a scope)
As my confidence in the rig grew, I might bias the amp hotter and hotter until distortion showed up and then back off. I myself bias my amps a little on the cold side, but I am a jazz player and use a clean tone. I'd rather my tubes lasted longer, but that's just me. Tweed amps are sort of not useful to me. YMMV.