I have never needed to use anything other than my Circa 1980s Silca track pump to get a tubeless tyre to seat properly.
I do brush some some soapy water on the rim, and rub a cake of soap along the tyre bead both sides, and that helps the tyre get onto the rim, and seat properly. I do this process without putting sealant in. I then let the pressure out, remove the valve core, then inject the sealant, replace the valve core, pump to about 30ish psi, lay the wheel on one side, then the other, and generally flip the wheel a few times in my hands so that the sealant coats the inside of the tyre carcass.
The new generation Conti tyres might prove more of a challenge, but every schwalbe and maxxis tyre has mounted for me without issue using that method.