When a teenager hit puberty, does that technically mean they are physically ready to have children?

Puberty takes time: Puberty is a transition period marked by a series of hormonal and body changes in both sexes. Some are obvious, like nipple growth in females & some are hidden, like testicular swelling in males. The transition can take from around 2 to 5 years. Reproductive ability requires ovulatioon for females, which can occur with the 1st period but often up to 1yr later. Males are capable mid process.

Yes.: Boys' sperm is viable very soon after any of it is produced, and girls can become pregnant the month before their first menstruation.