We are driving to Bellinzona from Antwerp. The most straightforward route would take us through the Gotthard tunnel.
How bad would this be on a Friday afternoon in June? I don't really see an easy way to avoid it.
We could take the pass, but I'd rather not on this trip.

Advice from Switzerland experts would be appreciated!

What do you mean with "how bad"?
It's just a 2way road with many trucks and heavy traffic after 4pm, but probably no waiting time at the tunnel entry.
If you come from Basel and must reach Bellinzona, the Gotthard Pass road would be the best alternative. All other itineraries would be much longer.

I mean delays of an hour or more. We would probably get there at about 2 pm on a Friday.

There are no holidays in June, neither in Switzerland nor in the adjacent German Bundesländer. The elections in Italy (if there are any) will not take place before July. There will be some additional weekend traffic, but usually in early evening and without notable traffic jams.

The queues are a regular feature on the headlines in Switzerland, at least in Ticino. At times the waiting times are terrible. I've done the tunnel many many times (in the past 2-3 years) and got stuck for an hour or so a few times. An hour is not the norm but it happens. More too. You stop, get off the car, in again, stop again, get off again, in again, etc.. often for 10 or so kms. I have always been told (and experienced myself) that weekends in April, May, July and August see the most traffic. We listen to the radio or check with the TCS and if the cues are bad we do the passo, it's always nice to see the mountains.

how long would taking the pass take? I drove it years ago and was wonderful but think OP wants quickest route - if up and over not much more a good option though that could be clogged too?

It is not bad. Just very long . I would not worry about it.

I think OP is more worried about delays not the tunnel itself!

The Postbus does Goeschenen - Andermatt in 15 minutes and Andermatt - Airolo in 40 minutes (with many stops). Individual cars take about half that time.
Waiting times at the tunnel entry: there are often queues during holidays (July - September, Easter, Whitsuntide, Christmas, National bank holidays in Switzerland, Italy, Germany, Benelux....) and on weekends (Saturday morning, Sunday evening).

The pass under normal circumstances takes less than an hour. An hour's wait is about 6 maybe 7 km of queues.

I should have mentioned that the times when we were stuck in cues were times when the pass was closed (landslides if I don't remember wrong as it wasn't winter). If the radio says 3-4 km queues we always take the pass if it's open. I can't remember taking the pass going south recently but we usually travel when everybody else is travelling.

Thank you for the information. We'll see how it goes and keep an eye on traffic information. We can always decide to take the pass last minute.
We're not really in a hurry, just want to be in Bellinzona in time for an aperitif...