No. The second option is the most logical, because no evidence either way is just that: no evidence
Only if we have evidence that Bigfoot does not exist, will the first option be the most logical.
That is different from what is most likely. It is still most likely that Bigfoot does not exist. (Which is why not believing in Big Foot is still a fair call.)
For example: It is suggested that Yeti might be a type of bear. Had we accepted that Yeti don't exist due to lack of evidence, then we'd never make the effort to make such a discovery. In fact, often we even reject any supposed evidence. But by accepting option 2, then the case is not closed until we have some evidence, one way or another.
Who knows what other "woo-woo" ideas might have some truth in them. I like to give the example of St Elmo's Fire. Of course angels don't dance on masts, but by at least looking into it, we found there was some truth behind the stories after all, and so we learnt something.
Disclaimer: I'm not a God believer, because there are so many easy logic traps that God simply doesn't make sense, at least not in any way I've ever heard of.