This was never explained, but it is possible if I am not mistaken the timeline. But I would say that most evidence points that it did not happen.
Here's the Timeline. From Wikia James Potter.
On 31 July, 1980, Lily gave birth to their son Harry James Potter, but
it wasn't long before Albus Dumbledore found out that they were in
In October 1981, Dumbledore told the Potters that their best chance
of remaining safe against Voldemort was the Fidelius Charm.
Wikia Alice Longbottom
So it could have happened as they were all friends. But they probably would have been a little more careful with the baby's around and it most likely wouldn't have included any Weasleys.
Molly Weasley couldn't be there.
During the First Wizarding War, Molly was not mentioned as a member of
the Order of the Phoenix, and indeed Lupin confirms this, but this is
likely because she was having and taking care of many young children
at the time.
However here are the reasons I don't think it would not have happened.
- They would have been trying to protect the baby's more
- They would have been in the middle of a war
- There probably wasn't enough time before they had to go into hiding and then were killed by Voldemort.
And if the above reasons didn't convince you then there are these ones.
- There would have been some evidence in pictures or something
- Someone would have told them. Probably at the same time the picture of the order was shown to them.
Did Harry meet Neville/the Weasley twins as a baby? - Cos Forums
They come up with some valid points.
From user Voldemorts8thHorcrux:
Probably, it makes sense, but maybe they didn't want to bring their
children in risk of being hurt or in danger, or maybe it would be
safer in the first headquarters.
From user Tiberius:
I don't think so. There are plenty of members of the original order
who are still around who would have told them if it were true.
From user snapegirl:
If I remember correctly, the Weasleys weren't in the Order then, only
Molly's brothers were and they were killed. I guess it's possible
harry could have met Neville though.