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Lets say that all of the Genestealer Cults units in your army have the Deep Strike Ability.
Although this is probably not a great tactic in all games, humor me...
What rules are currently in place in 10th edition to prevent your entire GSC army from not showing up at all until Turn 2?
Is there a "boots on the ground" equivalent somewhere?

Depends upon the Mission Pack. The Only War Mission Pack "The battle ends when all of the models in one player’s army have been destroyed, or once the fifth battle round has ended (whichever comes first)." Other mission packs will have their own rules.

Deep Strike:

During the Declare Battle Formations step, if every
model in a unit has this ability, you can set it up in
Reserves instead of setting it up on the battlefield.
If you do, in the Reinforcements step of one of your
Movement phases you can set up this unit anywhere
on the battlefield that is more than 9" horizontally
away from all enemy models.

PLACING UNITS INTO
STRATEGIC RESERVES
Before the battle, when you are instructed to Declare
Battle Formations, you can select one or more units
from your army to be placed into Strategic Reserves
(excluding Fortifications).
The combined points value of all the units you wish
to place into Strategic Reserves before the battle
(including those embarked within Transport models
that are themselves placed into Strategic Reserves)
cannot exceed 25% of your total points limit for your
chosen battle size, as shown in the table below

That one also expressly calls out that Deep Strike is not Strategic Reserves.

I expect it’ll be in the Matched Play Mission Pack when we get it.

Yea in rulebook no t1 prevent.

Then again same was 9e. T1 was mission pack prohibition

You can, for eternal war from the core rules, start the game with no units on the battlefield and all can arrive T1. The GT cards may have rules prohibiting this.