That would be the expected answer if one asked, "Is the harvest of a sasquatch legal?"
That's why that question is not to be asked. You want the permit, which makes it legal to kill one.
Your harvest permit application must include a section listing reports documented in the area you propose to hunt and your complete reasoning why you believe they are in that area, including food sources, expected seasonal movements, etc. This establishes the baseline that they're there, not if the agency acknowledges it or not. If they insist that they don't exist, their reasons for refusing the permit also don't exist.
Your plan to harvest one is outlined, and you request a permit to do the deed. Force them to deny the permit on the details in or missing from your plan, which you then circumvent with a solution. For example, they say that you might shoot a man in a suit. You counter with the argument that your operation will not be publicized (another likely plus, from their point of view), so hoaxers won't know you're there. You will also have an experienced and licensed hunting guide on your team to oversee the actual shot if the agency insists.
The entire goal really isn't to shoot a sasquatch, or incur the costs of doing so. The goal is to corner governnent into documenting the reasons why they refuse to allow anyone to fulfill the demands of science to provide the carcass, or corner them into the requirements to do so, whether that is on private or public lands.