The way to cope with events like this is to turn your attention outwards, not inwards.
At the moment, your attention is inwards, you're worrying about yourself and how you will come across etc.
You need to find a way to turn your attention on to the people at the meeting.
For job interviews, I did this by reminding myself that it wasn't just about them judging me - I was also there to find out if the job was suitable for me, by being curious about the job and listening to hat they were saying and how they were saying it.
This took my attention away from myself and made me a much better interview candidate as I was asking intelligent questions about the job. It gave me a sense of purpose and this simple trick got rid of my anxiety in interviews.
As Bemur says, being new is a gift. No one will expect you to know much. Stop being so hard on yourself.
When you introduce yourself, make sure you mention you're new, you'll do your best to answer or refer on any questions and you're looking forward to working with them. Don't be apologetic about being new, just factual.
And then make it your mission in your head to get to know who the people are in the room and how they fit into your work. Listen to them. Ask questions if it's appropriate, or make notes if not.
7.5 hours is a long time to fill!
Maybe give yourself the challenge of finding out each person's name and job title and writing yourself a note about each - perhaps one note on how their work relates to yours, and another on their topic in the meeting - or whatever it would be useful to have afterwards.
This gives you something to do.
You don't have to use the specific examples I've mentioned here, but the key is to get your brain to focus on something purposeful and not yourself.