Can a US citizen change from Visa Exempt Entry to a Type B visa in Thailand?

You won't be on a visa on arrival, you won't be on a visa of any sort. You will come in visa exempt. Whether you can change to a non-b or not will be up to your employer and immigration office

As a US citizen you didn’t get a visa on arrival. If you entered with no visa you were given 30 (or 45 days) for free using the visa exempt entry scheme. Whether you could change that in country to a non B will be between your new employer and the local immigration office. Almost certainly the answer will be no, as the paperwork needed will be way more than applying for a non B at a nearby consulate. In theory it could be done, but in practice rarely. They did change some teacher positions in country and perhaps may still do but it’s rare.