First ask your bank if it is possible to accept a cheque in US dollars. Some won't but some will, possibly for a fee.
Second ask your bank if there is an account you can open that would take a US dollar cheque. Lots of banks can set those up, again possibly for a fee. Try another bank in your country off they won't. This is your most likely solution.
Third ask the company if they can write a cheque in your home currency.
Fourth ask the company if they can write a money order instead if a cheque. They are similar enough that they might.
Fifth investigate what it takes to open an account in the US. If you are doing a lot of this it might be worth it. Your bank can probably help with this. They have partners and probably branches in the US.
Only then think about the process you are describing. It's going to be complicated so best to avoid it. You would need to get the cheque sent to you, endorsed, sent back, paid in, and then transferred.
While the above are my recommendations for dealing with a legitimate business, OPs second comments set off all my scam alarms. No bank recommends that a customer not use Paypal, and nothing the company says explains why they don't use a wire transfer, the obvious and simplest way of paying you. What they write is what a classic scammer says as to why they want to use the most easily forged method of payment in the world.
Unless this is either a large, reputable company or a company you have dealt with before I strongly recommend:
- Tell the company that if they insist on paying by cheque you will not be sending them the work until one month after the cheque reaches your account. Tell them that it will take a month for the cheque to process, and a further month to verify that it is valid. (The extra month is because a cheque clear doesn't mean it won't later be discovered to be a forgery -- see many other questions on this site for more details.)
- Tell the company they can have their work much sooner if they send you payment by wire transfer or another secure method. It's their choice.
- The stronger they argue that cheque is the only option and you MUST send the work immediately the more certain you can be that this is a scam.
- Do not under any circumstances send them money, even if they 'overpay' you or claim to need some sort of fee to enable your payment.
- Mentally prepare yourself for the possibility that you will not be paid.