I disagree a little with some previous comments:
I say suck it up and take the 7.98% especially if you think you will refinance in 6 months. 50K over 5 years difference per month approximately $116 and you will be paying more interest and less principal each month, but try and suck it up and then refinance in your own name.
It's a huge ask to have someone co-sign no matter how willing they are to do so.
Let's say something bad happens, which I would never wish on anyone. Let's say cousin's marriage ends and he finds himself in a differnt financial position because he must pay alimony and support 2 households and pay child support. Having this $50K loan on his name could restrict his ability to get additional financing.
Also another g*d forbid situation let's say something happens to you an unexpected catostrophe and he's stuck with a $50,000 loan till it's paid off.
7.98% is certainly much more than 2.98 but it's not the end of the world.
I understand you are new to the country and building your credit and family steps up and helps family. If it meant the difference between getting a modest reliable car and not being able to get anything then let him co-sign but to have a $50,000 loan that someone else has joint responsability for IMHO is not the right thing to do.
As a doctor it sounds like you make good money and can easily afford the payments and if you must have that car that gives you the $50,000 loan then consider sucking it up and paying the extra interest for the 6 months until you refinance.
Remember however cars depreciate new ones much faster than used or CPO and if you do not put significant money down you will not be rightside up on the loan in 6 months or even a year or longer and won't be able to refinance it.
Lets say car is $55,000 out the door taxes and fees included. and you put $5,000 down Well taxes alone are probably $3,500 and the other $1500 will cover fees and maybe give you $750 as a real downpayment.
Even the best credit unions will only finance up to 120% of the book value.
In 6 months you will have paid down $4,000 or so but will the car be worth 120% of it's value
This Carfax site https://www.carfax.com/blog/car-depreciation says cars can lose more than 10% of their value in their first 6 months.
However you could always come up with some cash then to get it below 120% Loan to value.
Co-signing is really an unfair burdeon that should be saved for true emergencies and the right thing to do is to at least rethink things as you have options.
Some exceptions but rare and usually only subprime lenders take credit card payments.
Regional Acceptance does Santandair did but changed it.