No, the “no romantic attachments” rule didn’t appear explicitly until Attack of the Clones, although arguably a more nebulous form of this rule was hinted at in Phantom Menace. But the OT definitely never even considered the idea of “no romantic attachments” as a possibility. The pre-Prequel EU of course never considered this idea either, and thus we had Jedi getting involved in romance like everyone else (e.g. Mara Jade, etc.).

You can argue further (as you point out) that the OT not only doesn’t have this rule, it outright contradicts this rule, since we hear that Anakin had offspring and the movies never indicate this was in any way weird or not expected of a Jedi.

Also, having offspring is possible without romantic attachments. The Jedi rule is specifically about romantic attachments. Arguably, some species that say, reproduces by laying eggs and then just abandoning them (as is done by many species on Earth) would be allowed to be a Jedi AND have kids.

There have been a couple of in-depth discussions about this issue in previous threads in this forum.

The general consensus around here is probably that romantic attachments were allowed until George Lucas decided to inject some Romeo and Juliet into his love story, because he didn’t know how to write a love story. I mostly agree with this sentiment, but consider it a bit too reductive, since arguably the “no romantic attachment rule” could be considered a logical consequence of the Jedi’s general dislike of emotional attachments, which was implied (if somewhat muddled) in The Phantom Menace when they bring up Anakin’s fear of losing his mom.