I would avoid being what might be seen as too pushy to be honest.
Wait until you move in to do anything. On moving day, go about your business moving in and you may well find that neighbours pop out to say hello. That is the best way really. Sometimes people won’t do that on the day as they know lots is going on for you and don’t want to interrupt you. If you’re in the front garden next day or still moving stuff about, they might appear to say hello at that point.
And if you’ve been there a couple of days and been going in and out a few times, with no sign of neighbours, at that point drop a note through the door with your contact details and a brief, cheery hello.
Dont go and knock in the current climate of Covid. And definitely don’t go and knock before you’ve actually moved in.
It’s great that you’re friendly but you need to be sensitive to the fact that Covid makes people nervous and some people just aren’t into neighbourly friendship. For some, a ‘hello’ or wave when getting in the car really will be pushing it for them. People also like to feel they are able to develop contact or not on their own terms and not have it pushed on them. So be careful with the door knocking or taking stuff round. You need to be prepared to let them take the lead and be guided about the amount of contact you’ll have by them and respect that, rather than pushing yourself on them.
We had new neighbours move in just before Christmas. We had a friendly relationship with our last neighbours and would take in parcels, lend garden equipment, had the odd drink in their garden in the summer and used to chat over the fence if not in a hurry when heading out.
The new people moved in on a wet, dark afternoon when Covid restrictions were mounting. We could see them moving in from our front window and resisted going out to say hello because we knew they’d just want to get their stuff in. The next morning, they were moving stuff in and out and into their shed etc and DH was in our garden and moving stuff out to the bins. He said hello and I could hear from in the house that he was chatting to the man who had just moved in. When it had gone on for 5 mins, I popped out and said hello too. If the conversation between DH and neighbour had only been a minute or two, I wouldn’t have popped out, taking the cue from them that they didn’t want a big chat or not at that time.
Winter and Covid makes it hard. 6 weeks on, we’ve now chatted about 4 times whilst heading out for a walk. They are friendly, ask about the neighbourhood and we know where they work and about their kids. I’d imagine, that come the summer and nicer weather and less Covid restrictions, we might ask them into our garden for a drink...because I can gauge from our chats so far, that they’d be up for that. Just something low key and brief. And it won’t be a frequent thing....we want to be friendly neighbours but not great friends really.
It’s good to be friendly but not too pushy and to be willing to take your cue from them.