I was watching this video and at this point he said that since gravity is not a force as per GR, we are left with only these normal forces pushing you up that accelerates you... but I don't understand this as newton's 3rd law mentions pair and if gravity is not a force then these normal forces shouldn't exist at the first place isn't it? Where are these forces pushing us up with acceleration of 9.8m/s2 coming from? I understood that we need to be in accelerated frame of reference just to stand still in curved spacetime as he says in video but from where are these normal forces coming from that is giving us acceleration?
newton's 3rd law mentions pair and if gravity is not a force then these normal forces shouldn't exist at the first place isn't it ?
This is a misunderstanding of gravity and normal forces work in Newtonian gravity. The normal force is not the 3rd law pair of the gravitational force.
The normal force is the 3rd law pair of the contact force that deforms the ground. If you are standing on soft ground then the 3rd law pair of the normal force is the force that leaves your footprint in the ground.
If you decide to jump, then the gravitational force remains constant while the normal force increases dramatically. The effect of the increased normal force is to accelerate you upwards. The effect of the increased 3rd law pair of the normal force is to leave a deeper footprint.
where normal forces coming from that is giving us acceleration coming from?
The same as in Newtonian physics. Your footprints show that you are compressing the ground. The third law pair of that compressive force on the ground is the normal force on your foot.
The only new thing is that spacetime curvature makes it so that “straight-line” inertial motion converges. Where it converges things runs into each other and exert the usual contact forces.
Newton's 3rd law describes how a single force is a two-way interaction between two objects.
In this it simply says the normal force acts on your feet with, say, 700 Newtons, and the normal force also acts on the ground with 700 Newtons.
I consider Newton's 3rd law to be nearly self-evident (for people with a modern education), and it doesn't really tell us anything profound.
In contrast, the sum of forces that you perform on a single body concerns Newton's 2nd Law. Or in this case the geodesic equation as we are discussing general relativity.
But a one-sided unbalanced force like a rocket in space is perfectly allowed. In the case of standing on the Earth the curvature term involving $\Gamma$ is perfectly balanced by the normal force, so no net motion occurs.
Let's say you're standing on a table. The table applies a force to you to keep your path deviating from a geodesic, or, in a non-inertial frame called...everyday life...to counteract the fictitious force we call gravity.
Of course, you also apply a force to the table, which could break if you're too heavy.