I think that you are assuming the big American companies would conduct their day-to-day business in English, and this usually isn't so unless the company is in a country where fluent English is common or the norm, such as the Netherlands, or the language is extremely difficult to learn, such as Japan.

Organizing a visa would cost a company time, probably lawyer's fees, and the visa fees on top of that. No one is going to go through that unless you have something special to offer. Why go to the extra expense? Especially for someone who just wants to get the feel of things.

One option that might be open to you is to work teaching English as a second language. I'm told it isn't well paid, and most teachers juggle classes from with several different companies, and spend a lot of time on busees. People used to do it illegally but I don't know if that is possible any more. It would be one way to bring in some money while you learn the language.