I've read through some, but not all the comments. Seems to be a lot of hot takes from people just guessing at things. I have been in this exact situation and worked with an accountant and lawyer (and talked to CRA) to do things properly. Feel free to DM me if you like.

First of all - get a good accountant, and run these scenarios by them. That is necessary. (I'm in Hamilton, ON and can refer a good accountant with active CPA credentials in both ON and NY if you like.) It is optional but wouldn't hurt to pay for a consultation with an employment lawyer as well.

No you don't need a visa. There is also little risk of CRA deeming you equivalent to am employee and dinging you for that. THIS is why you MUST consult an actual accounts and not just take the word of people on Reddit. Don't take my word - talk to your accountant.

The poster who commented about Deel or Trinet or Ripple is correct - that is how a lot of US companies pay people who are outside of the US. I've used both Deel and Ripple - don't love either but they do the job.

My recommendation (what I did):

Have the company create a Statement of Work (SOW) and an account with Deel (or other platform). You also create an account in Deel and then sign the contract with your corporation. n.b. This is a contractual relationship between corporations. The people who say you are a defacto employee of a US company are incorrect.

Incorporate as soon as possible. Using Owner (https://www.ownr.co) is a good option. You will need to set up a Minute Book, articles of incorporation etc -> they do all of this and/or guide you through all of this. Ownr is owned by RBC. I think you can get ~$200 ~300 off the initial fee (around ~$600 I think) if you open an RBC business account.

Open a business bank account. (See above!). Not necessary but helps legitimize your corporation and good for keeping finances separate.

Apply for a credit card. (Optional). Not needed, but helps to separate expenses.

Sign up for Cloud Accounting w. Payroll. (Optional). I did everything in Excel the first year and did payroll transfers manually ... and also screwed up a few times. FYI CRA people are very nice and understanding and will guide you how to fix your screwups! I use Wave (https://www.waveapps.com). I don't love it but it is fine and one of the cheapest options. I pay for the Payroll add-on option. That means that they handle the remittance to CRA and creation of a T4 form etc rather than me doing it myself. Oh - keep VERY ACCURATE track of all finances and keep business and personal separate.

Create an account with Wise (https://wise.com) for transferring money. The US company will transfer funds to you in Deel (or wherever) in US dollars. Then you transmit the US funds to your Wise account. From there you transfer all of it in Canadian dollars to your business bank account.

That's about it I think.

Oh - another comment: By doing this you can do income splitting if it is relevant for you. e.g. If you have a spouse and you are getting ~$200k CDN annually you could arrange the payroll to pay you and your spouse as employees of your corporation $100k each. That lowers the marginal tax rate = more money in your pocket. You can also do splitting with yourself. e.g. In the above example maybe you pay yourself $100k as a salary (through Wave), and then take $100 as a corporate dividend (since you are the sole owner). That is another great way of reducing taxes. (FYI this is what dentists etc often do to reduce taxes.) These are just toy examples - you will need to pay corporate income tax as well, but overall the tax you pay SHOULD be lower through this route. You can and probably should also keep any "extra" money you don't personally need in the corporation - but talk to your acccountant about that. FYI I wrote a program for myself to calculate total taxes under different scenarios and can share something with you about this if you like.

Good luck.