Roger’s crew disbanded 25 years before the current storyline and Roger was executed 24 years before the current storyline. There is an entire year gap where Roger’s actions would have been completely unknown to his crew. Additionally, judging from Rayleigh’s exposition in Sabaody it seems like not even Roger’s right hand kept in contact after disbanding.
Now, I’m not really against Roger’s crew knowing Roger wanted a kid. One of the more recent chapters seems to hint maybe that could have been common knowledge amongst the crew. However, once again no one except Garp and whoever Garp told would have known Roger’s kid was a boy let alone one East Blue.
Tbh, it’d be even more likely that Roger somehow kept this kid safe through his own means as opposed to entrusting the child to Garp.
One big big thing to note is both Rouge and unborn Ace were in South Blue even following Roger’s execution for over a year. If any of Roger’s crew were privy to that information they likely would have given Rouge and Ace shelter. Garp didn’t come for Ace until after Rouge gave birth.
Lastly, Roger had other options than Garp from the perspective of someone who hasn’t seen Roger for a year (i.e. Roger’s crewmates). Whitebeard is one such option.
This is the reason “foresight is always 20/20,” is a saying. Looking back, it’s “obvious,” or “easily deduced,” Roger entrusted his kid to Garp when you haven’t really taken into account all the factors going on during that time period.
Roger’s crew seemingly (judging from Rayleigh) had little knowledge of Roger’s actions and no contact since they disbanded. Roger seemingly didn’t reach out to any of his crew to take care of his kid and instead entrusted the child to Garp. Assuming Roger entrusted his child to someone else as opposed to simply ensuring his wife was safe Whitebeard, Roger’s other prominent rival, would be as good a guess as any. Being that Oden shifted crews and both Roger and WB had several run-ins as well, Roger most likely would’ve known WB’s lean towards family.
For me, I most likely would’ve assumed Roger actually made sure to secure his wife’s and unborn child’s protection before turning himself in.