However, ignoring the need for a rocket, theoretically a cow would produce enough methane in its lifetime to propel it into low earth orbit twice. From an earthlings perspective the cow could then appear to jump over the moon

Good question. The methane produced by a single cow in its lifetime is far less than what's needed for a lunar mission. In fact, it would take approximately 22,545 cow lifetimes to produce enough methane for a single lunar mission using current rocket technology.

Estimated average single cow emits 100-120 kg of CH4/yr. Total 264t CH4 in Starship is closer to emissions of about 2,500 cows/yr. [@perplexityai.bsky.social]
Also some of the CH4 probably burned in the explosion so the actual CH4 release to the atmosphere would be less.