Temporary visitor to work visa

I've been offered a position at a company that wants me to complete the work visa process from within Japan. From what I've read, the only official way to receive a work visa is to receive a CoE and apply for the work visa within my own country of residence, then head to Japan after I receive this. (I will not be working for this company until this process is finalized, as that would be illegal)

I've also read that people have gone to Japan on a tourist visa and applied for a change of status to a work visa and have been successful. And that for a temporary visitor, usually some other extraordinary circumstances should be present (but that this is often not enforced).

I really like this company, but I am nervous about entering and having my application denied because I did not apply for the visa in the U.S. Does anyone have experience doing this?

The issue with application for Change of Resident Status from within Japan, with work status in particular, is that you cannot start working until the new work-permitting status is granted, and that can take a bit of time. So while you (and the employer) wait for that, the employer cannot get you started, you cannot start work, meaning cannot be paid either). Do you have enough savings to tide you over a few months if you have to?
You might want to ask your employer how long (based on their experience) it takes for the change. Also you might want to find out if they are planning to give you any training in person (thus in Japan) before you start working there.

By any chance, is the company Epion?

I did go to Japan on a temporary visitor (tourist visa), then applied for a long-term visa while in Japan. I do not think they check whether or not you applied before.
It took about 6 weeks to process the long-term visa. During that time i wasnt officially working, but could enter the building and sit at my desk. I dont jnow what you could arrange with your next boss.
Be aware that when entering on a temporary visa, you need to have a return flight planned to leave Japan before the 90 days are over. I did not, so that was quite stressfull. They did not let me in without the return ticket, only after some phonecalls with my boss in Japan I could enter. So have some phone numbers and a printed letter of invitation within your hand luggage, in case you go without the return flight.

And that is the risk and maybe others that you might encounter.
Not just at point of entry, also when you do Change of Status.

Period for Change of Status can varies depend on situation.
Think of what will you do or expenses that will incur during that time?
Will you company help you out with living and expenses since you are not allowed to work, so no income?