Managers and senior employees in many organisations use consistent lateness for meetings with their juniors as a status symbol.
The message is "You have to wait for me (but I never have to wait for you) because my time is more important than your time; I'm more important than you". If there's a group of people being forced to wait then the message is even stronger: "my time is more important than the time of all of you put together".
This kind of thing is particularly endemic in industries which are traditionally very hierarchical - in the medical profession for example, it would be quite common for a consultant (senior doctor) to be late for a meeting with a nurse, but much more unusual for a nurse to be late for a meeting with a consultant.
This is influenced by cultural factors of course - when I'm saying "late", what I really mean is "later than the other meeting participants consider the normal time for arrival". (In some cultures everyone arrives 15 minutes late for everything).
Notice I'm saying consistent lateness here - one-off lateness doesn't have the same implications: the train can be late once or twice and that's normal, but if the train is late every week and I don't aim for the earlier train, then I'm sending a message about how I perceive our relative importance.
Many men in business measure their masculinity in terms of how late they can be for a meeting. For them, arriving on time would show you were extremely junior or that you had so much free time that you could afford to sit around waiting for other people to show up. Being late to a meeting shows everyone in it how little time you've got and how lucky they are to have someone so in demand at their meeting.
Office Politics: How Work Really Works, Guy Browning 2006
So - what to do?
The most important thing is to bear in mind that you're the new guy and therefore the lowest-status person present. If this is a workplace where status is important to managers, then the last thing you want to do is to be seen to undermine their status - they won't like you for it.
So don't say to them:
"Hey guys, you're behaving quite self-importantly here. I know you're probably not doing it on purpose - it's probably unconscious - but please knock it off".
Instead, best to deal with the idea that they want to pay you to do nothing for 20 minutes once a week, simply in order to flatter their egos. It's not mature behaviour and it's not effective management, but you're not in a position to be able to point this out without doing yourself a disservice with the people in charge of you. And nobody likes a smartarse.
So here's some options:
Simply do nothing for the 20 minutes. If that kind of ego-massaging is the work they want from you - and it's pretty easy work, after all, and not really all that demeaning - then give it to them.
Bring some work with you to the meeting. Take your laptop and do some work until everyone arrives. That way you're using the time productively. (This is better than intentionally arriving late for the meeting yourself, because it's less risky for you as the newbie).
Use the fact that you're waiting there in the room with your junior colleagues every week to improve your personal relationships: chat about sports, families, holidays, technology, whatever it is that they're interested in.
Use the time to discuss work-related topics in advance of the meeting: this is your best option. Don't get out the agenda and start conspicuously talking through it point-by-point in advance of the manager's arrival - that could look bad - but instead just chat about what you know is going to come up in the meeting. This prepares you for the actual meeting itself by already knowing what some of the people present are going to say and what angle you should take. It can be incredibly useful. If you want to do it subtly, you can mix it in with the personal chat ("did you see sports team's event last night? Oh, and what do you think about project thing?"). Pre-meeting meetings are a super-valuable tool, and can become the place where the decisions are really made - if you and your peers get good at this then you can start sewing up the major decisions before the managers even arrive. ;)
By the way, I'd consider this kind of asserting of status by managers and senior team members fairly unusual - and somewhat dysfunctional - in a software engineering setting. For me it would be a red flag for an organisation that's maybe more bureaucratic and status-conscious and less delivery-focussed and meritocratic than it should be. That does vary by culture (around the world) though, and anyway it's essentially the CEO's problem rather than yours.