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Guess what? You get to reinvent modern metrology!
I'd start with making a surface plate using Whitworth's 3 plate method.
Next, make a perfectly square block, pick two opposing faces of that block, that's your unit of length. Use your surface plate to make more and measure things against it.
If you're really smart you would have made that block out of some sort of homogeneous material like steel and made it a perfect cube, not just perfectly square. That's going to be your prototype weight.
Temperature is the easy one, make a thermometer. Mark where the liquid is at based on two different repeatability phenomenons. Subdivide as desired. Someone will come up with a "better" way later.
Time is another easy one, just build a pendulum and start counting.
That sould get you through most of the neo-industrial revolution.
The rest of the base units will come later for now focus on building a lathe.