Yes, but that's not problem of meat, just farming.

If we were farming sustainably (only grass fed etc.) we wouldn't be able to produce as much meat as we do today. Which implies that on average everybody would eat less meat. Much less.

Grasses that have been developed for pastoral farming still lead to more methane burps. Current research seems to be focused on breading grasses / other pasture crops, and breading animals that produce less methane, Vaccines that could be given to animals, Inhibitors that could be added to their diet[1], and modeling of the methane formation process. But yes, the simplest way to reduce it would be to reduce the number of animals, by eating less meat.

[1] https://www.pggrc.co.nz/files/1501479614891.pdf