How long does it take for a stage 1 gastric signet ring cell tumor to grow into a stage 4?

No one knows: Cancer is staged when it is discovered. You may have a cure. Or there may be cells hiding elsewhere, as in the liver, that will grow into metastases in a month, or five years from now. "stage" is a most-optimistic-possible-scenario assigned by the physician to guide treatment. I wish you luck and appreciate your proactive approach.

Variable but mos-yrs: While tumor growth is always variable based on how aggressive the cells are when they first develop, typically early stage cancers are less aggressive and therefore a lower grade than more advanced tumors seem to be once they've accumulated more mutations as they dedifferentiate. That being said cancers grow and advance and most gastric ca's will take many month and even a year or so to spread.