You can remove most of the bubbles without using a pressure pot.
For resin:
use slow setting resin, mix it in a larger container and set it away to let most bubbles escape.
You can vibrate the bubbles away, for example using a sanding oscillator powertool.
Draw the resin into a syringe by dipping it all the way down, so when you draw the piston no air gets in.
Do not let any air get into the syringe when drawing.
Inject the resin into the mold at the lowest point, slowly, preferably using blunt tip needle.
I grab the highest diameter needles available in the pharmacy, usually 0.8mm, and trim them with a dremel and a cutting disc to 2/3 length. This also decreases flow resistance.
Do not empty the syringe completely, because there is always a little air trapped on top - when you draw the resin in, the nozzle always has some air in it.
This will most likely not work for optically clear resins due to microscopic bubbles that won't be able to escape.
For silicone:
same as above, but it's hard to inject it via syringe due to its viscosity.
Pour it slowly from the container, keeping a very thin stream - this will pop most of the bubbles that remain. Pour into the lowest point. This can still form cavities on the undercuts, you can help it flow into the undercuts with a toothpick, a cotton swab, or a small brush.
You'll get much better results with a pressure/vacuum pot, though.
You can scavenge a cheap and silent compressor/vacuum pump from an air conditioner, or a refrigerator.
It works both ways, so you can use it as a vacuum pump and an air compressor.
There are a few tutorials on that floating around youtube.
I think there are commercial solutions based on these types of pumps as well.
You won't have to run the compressor for a long time - you just need to keep the pressure constant for the resin setting time.
Normal market-bought compressors usually have an intermediate air tank that gets pumped up to the compressor's nominal pressure, a pressure switch that turns the compressor on and off when the tank reaches certain pressures (max/min), and a pressure reducer, often with an integrated deoiler and dehumidifier.
The compressor will only turn on if you have a leaky pressure chamber, and the compressor will have to compensate. It will run for a bit to rise the pressure in the chamber to the maximum value, and turn off again.
For the pressure chamber itself I recommend this thread:
https://geekhack.org/index.php?topic=96853Cheap, scaleable, and very very fast.
You can also use centrifugal casting as an alternative:
It comes with its own issues though.