Just wanted to know (my account is under 30 days old) how many days old does a Sylesti have to be to reach adulthood?

For pet aging, it depends on what stage the pet started with when it was created. For starter pets, they should take about 18 days. Also, the lifestage of the pet is dependant on maturity, and not the "age" shown on the profile page, which keeps track of the days since the pet was created,

To know the accurate maturity, you'll need your pet to be genetically tested. (There are players in the breeding forum who offer free testing services). Copy the pet's url, and at the end of the link, there will be a &maturity=__. That number there would be the pet's maturity in hours. So when the pet reaches 72 hours, they will become hatchlings; 216 hours to be adolescent; 648 hours to be adults.

When you find/catch pets in the wild, they can start off at any random number. So you'll need to test them to be sure.

Generated pets/ starter pets start off as adolescents, so they'll start at 216 hours. If you use magical pies on them, it'll add on 144 hours, which is 6 days.

For bred pets, they'll start at 0 hours, unless you have referral points that you've put into increase the egg incubation. For eggs, you can tell their maturity by looking at the bar near the bottom of their page profile. There will be a __/72, which is the hours of maturity out of 72. Also, for every 5 nurture clicks for an egg will add an hour, while every 2 page views for hatchlings will add an hour.