The only thing you might need a specialty pump or compressor with a tank for is to get a tire to initially start holding air. Once it starts holding air, any pump including a floor pump or even a mini-pump can be used to complete the process. There can be a big gap between the bead of the tire and rim that lets air out more quickly than you can pump it in. This can even be the case using a compressor/tank. What I find can be very helpful is to install the tire with a tube, inflate it to normal or somewhat higher pressure, and leave it overnight or in you warm car for awhile. This get the tire to conform and assume its proper shape. After unseating one bead and removing the tube, I can often get a tire to start holding air and fully seat o the rim just using a normal floor pump. Removing the valve core will help speed/ease inflation. Once seated, I let the pressure out, put in the sealant, then put the valve core in and inflate to operating pressure. Note that tires have a witness line molded into the sidewall just above where the edge of the rim would be when properly seating. Check that is this is visible and constant small distance from the edge of the rim all around both sides of the tire when it’s inflated.
As already mentioned, CO2 is generally not good for sealant as it creates carbonic acid in the tire which starts to neutralize the ammonia used in many sealants to keep the latex from congealing in the tire. This is where Stanimals comes from.