It's not easy to give one definitive answer - it's never really absolutely and completely safe, even healthy adults could get infected by pathogens transmitted from the cat. On the other hand - we humans, as species, don't derive our evolutionary success from obsessive avoidance of pathogens.
Also, a baby could potentially get infected in a wide variety of settings not involving this cat at all. For example a cat, especially outdoor one, could potentially transmit Salmonella - but a child could also happen to get infected with Salmonella while playing in a sandbox and putting fingers in the mouth, so it's wise not to become excessively focused on the cat in this context.
Depending on the source, one could find information that human immune system doesn't really mature until a few months of age, but also that it doesn't reach its full potential until adulthood. It isn't because either of these statements is wrong, it's just that the subject is extremely complicated and both of these statements are true in their respective contexts. I'd personally say it could generally be considered safe once the baby reaches a few months of age and isn't known to suffer from immune system disorders, but it's just my opinion and I'm not a medical professional (at least yet) as well.
As Trond Hansen suggested in a comment, having your baby vaccinated probably isn't really that important, because the vaccines of immunization schedule are targeted for diseases which are transmited from human to human, and aren't known to be transmitted by cats (for example hepatitis B, as the HBV is only capable of infecting humans and higher primates), or do so only in extremely rare cases (for example tuberculosis).
Please also consider that the fact of your cat being outdoor increases the potential plethora of pathogens that it could transmit, and thus significantly increases the infection risk compared to what would be if the cat was to be indoor. Outdoor cats could prey on small animals, eat suspicious delicacies from garbage bins, etc. - all the related potential pathogens are then being methodically spread from mouth on the whole surface of cat's fur - seemingly and deceivingly clean fur - while it is grooming itself.
What is more, apart from the safety concerns related to pathogens - please take into account that all interactions between the baby and the cat need your constant supervision - not only for the baby's safety, but also for the cat's. And generally, all interactions between animals and children should be supervised if safety is to be the priority number one.
In conclusion, to get the most accurate and reliable answer I think it would be the best to just ask your child's pediatrican. They would have access to a lot of more specific data than we have there, and they would be able to examine and estimate the developmental level of your child's immune system in the context of this safety concern involving the cat.