I remember seeing some buyers looking for unlisted tokens, especially launchpad tokens or something similar where they've yet listed on any exchange in the past. Their offer can be quite attractive, especially if you can't find any liquidity on DEXes for various reasons. I'd suggest you avoid this type of deal if you can find the tokens on DEX, or if you're not dealing with any reputable traders. Which platform are you talking about btw? Do they offer a smart contract to ensure this deal will proceed?
If you want to buy the tokens as early as possible, I believe building a script or bot to look at the market and buy them as early as possible would be better (or participating in the launchpad/ICO/etc). This assumes you know the right contract address, can code, can run the code with no problem, and so on. Maybe try OTC on some reputable platform too if you want to push it even further, though I doubt they will list new tokens quickly. CMIIW.