Generally, the sooner you refinance student loans, the better.
By replacing existing loans with loans at a lower interest rate, you will save money in the long run and this will start with the very first payment.
When refinancing, you can also elect to use loans with long terms. By doing, your required monthly payment will be lower, all things equal. so you will benefit from additional budget flexibility.
You will need good credit and an income that lets you comfortably afford your expenses and cover your debt payments.