Whereas Islam and Christianity encourage proselytizing, Judaism emphatically rejects it. According Rambam/ Maimonides, we can see this as early as the Kingdoms of David and Solomon, where courts rejected Jewish converts.

Converting to Judaism still remains a daunting task, especially among more observant Jews.

Religion spread is not related to age, but to the conquests of the states it was practiced on. In the examples you provided: Christianity started in the Roman Empire, in which eventually it gained acceptance and spread through it vast territory and those of the states which succeded it. Noted among these were the Byzantine Empire and the Frankish Carolingian dynasty. Islam spread the same way initially through the conquests of the Rashidun Caliphate and succesors.
Once these states conquered new land, forms of pressure on the population with distinct amount of tolerance which ranged from increased taxes to outright extermination/displacement assured that over time these conquered populations would eventually adopt the state religion. In the case of Judaism, the territory held by the Jewish states of antiquity was comparatively small and it's rule too short to exert any significant influence in later ages.

Another distinction to be made, and one that helps explain why proselytizing makes sense for some religions and not for others, is that Islam and Christianity are orthodox religions - membership based on shared correct beliefs. Whereas Judaism (and Hinduisms) are "ethnic" religions and more oriented towards orthopraxis - membership based on bloodlines and shared practices/rituals.

The dispute between Paul and Peter points directly to these differences. Paul's arguments eventually won out and Christ was seen as a means of salvation to anyone and everyone, not just a Messiah for the Jews. That most definitely opened the door to the mission field.

A religious community comprised of people who firmly believe their message is universal and share an imperative to bring their Truth to everyone else is simply more likely to spread than one that remains exclusive and tribal in nature.

When you add in official sanction by the state (Empire)...like wildfire!