The fact that you are asking such a question indicates that you have doubts about the origin of the coins in your wallet. And since you have such doubts, it is better for you to refrain from transferring such coins to CEX. But if you can't do without CEX, then you should try transferring a small amount from your wallet and see how the exchange reacts to this.
yeah that's most likely the case.
but OP just mentioned a bridge and Blofin, as far as I know, Blofin is relatively new exchange, I've heard this one just recently but never realy looked into it too deeply. I think if truly where OP's money coming from is just from bridge or exchange like blofin, he'll be fine.
I think OP can just try to read the T&C of the exchange and see what kind of rules they imposed, as some exchange might be "quirky" in that regard.
best solution would be, as you said, send small money first and test the water. most KYC exchange usually have no problem getting deposit from smaller exchange like blofin though as far as I know.