I've read all your comments. I meet the joining criteria.
TBH, your opening post didn't do you any favours - you did come across as a neighbour not many would like next door, quite heartless and full of yourself and your super busy, no time for a new neighbour.
First impressions count a great deal which is probably why you've received a bit of flack here.
You do come across as quite judgy and jumping to conclusions, with quite an inflated view of your role in all this.
When it comes down to it, all that happened is that a neighbour asked you to have a cuppa with his isolated, lonely, non English speaking new mum. You then proceeded to make lots of assumptions about him, his wife, your role, future scenarios and outcomes.
He asked you to make his lonely wife welcome and go over for a cuppa. That's it.
Frankly, yes, you do come across as a horrible person. And an awful neighbour.
Their last reaction is totally unsurprising. If also politely close the door with a no thanks. If you come across a fraction as negatively IRL than you do on here, he clearly got your sentiment and feelings towards him and his new family.
Our new neighbours (both foreign) moved in around 2 years ago. Within days of them moving in, we put a card through the door, welcoming them, giving our names and asking to let us know if they need anything, adding that most of us on the terrace know one another and are a friendly bunch. A week or 2 later they replied, thanking us and saying they were looking forward to getting to know the neighbours and neighbourhood.
There is no way I would have waited months before introducing myself. And I certainly wouldn't think negatively of a husband caring enough and brave enough to ask a person he doesn't know to be friends. It's not easy to do.
You can protest all you like and, yes, you thankfully took advice from here and went round - but still with negative outlook - basically to show willing under duress, however you know that you acted unnecessarily badly to the situation.
All you had to do was say welcome. Of course I'll come round for a cuppa. I work full time and it's a pretty full on job so during the week will be difficult, but when restrictions ease, husbans and I will come for a proper chat and a cuppa. I'll bring cake.
That simple