Do you mean for when you immigrate to the US? If that’s what you mean, I highly doubt you’ll be able to get travel insurance —as it’s for travel, not immigration. In most states they will ask for a SSN when you enroll on health insurance but it’s technically not mandated in most states, they just make it sound like it is, when really they care more about proving residence. In some cases you can use an ITIN. Besides, you would get a SSN soon upon arrival since you’d have a green card.
Do you have an interview date or are you still years out? I think it’s like a 10 year processing time for f-4