Will skipping nonce enchance mining performance given there's more resourceful miner As most miner program start with 0 nonce and increment from there, given there are many resourceful miners who will also compete for the same desirable nonce:

Everyone is mining at [0 ~ LARGE_RANGE] (lower range)

I mine at [LARGE_RANGE + 1 ~ MAX_RANGE] (upper range)

Scenario 1: Other people found the desirable nonce at the lower range, they do it way quicker than I do even if I were to mine on the same range.

Scenario 2: The desirable nonce is at my range and I found it first(before others found it since I skipped the lower range)

Is this a possible way to improve my mining performance?
The blocks you try to mine will have your block reward address in them. The blocks other people try to mine will have their reward address in them. Because the blocks are different, any correct nonces will also be different.

When you mine, you are not competing with other miners in the same search space. Whoever finds their own nonce first wins, but everybody is looking for a different nonce.