I think first Tuesday is families day.
People who say beer tents are fine during the weekday at daytime/lot calmer haven't been enough.
This year on the first Monday some of the tents were already locked shut at 2pm due to overfilling.
If there is the first sign of rain people hit the tents. They soon fill up.
I was in the Löwenbräu at 2pm on the first Monday and it was packed.
I've been going for 20years (every year)
Back in the day actually took my daughter in the Löwenbräu in her pram (1993) - had a whole Box to myself
Can't do that now.
Best thing is to aim for midday for an early lunch. Try to get a table in one of the boxes (generally areas not on the main floor - located at either end and on one side. You also have the Gallery - upstair so good view).
About 10 years ago took my kids during the week and chose a gallery area.
These tables are generally reservation only but often many only reserved from 4 or 5pm. It is ok to occupy a reserved table up until reservation time.
Being in a box area means a little bit safer - however hope you don't have to run the gauntlet of taking the 3 year old to the toilet. The toilets are at the rear of the tent.