non resident bank account

KBC is an excellent bank. Try them. There may be restrictions if you don’t live here or plan to live here.
https://www.kbcbrussels.be/retail/en/expats/discover-our-tailor-made-pro...

I've been happy with Beobank.

I tried to open an account for my son in anticipation of him moving here later this year and I could not do it. They would only open an account once he is resident and told me that this is standard practice throughout Europe.

You should have kept your old bank account open. If I were you I would try your old branch, write to them and see, as they will have some records of who you are.

Anyway notwithstanding that, do you have a specific reason for needing a Belgian account (i.e. you still have property here or investments or whatever)? If not, I think it's unlikely anyone will open an account for you. The "know your client" rules means that opening non-resident accounts is complicated and I suspect that all of the high street banks will turn you down. I also doubt you'll be able to open one of the online accounts, as one of the first things they ask you for is a copy of your ID.

Given that Belgian banks don't really work on the basis of a branch network (and most have reduced the number of agencies that they support in recent years), I would write to the customer services department at the HQ of your former bank saying that you now realise that it was a serious mistake to have closed your former account with them when you left Belgium and whether it would be possible to reopen that account. As well as giving details of your former account, you should also give your Belgian national registration numbers (which never die even for those who have only ever been residents rather than citizens) and send copies of the relevant page of your passports. I assume that you aren't American citizens because if you are you can more or less forget the idea, most Belgian banks aren't keen on having Belgian resident citizens who also happen to have American citizenship, let alone other Americans.