Just wanted to add to this from the perspective of someone currently going through the IVF process (I'm 37).
Realistically, it's likely going to be difficult for your partner to naturally conceive at 43. I don't want to make you feel negative, but when you have a limited window, it's important to be realistic. I'm currently going through IVF due to infertility, as are 3 of my friends, who are aged 40, 41 and 41.
@Jeanne Adil made an excellent point re the risk of giving birth to a child as an unwed mother - so it definitely sounds like you should prioritize marrying first of all, before anything else.
I would then recommend starting IVF in Iran. By all means, try naturally first of all if you want - but I can't express this enough - don't waste a lot of time on this. At 43, your partner's chance of naturally just conceiving is less than 5% - and that doesn't even factor in the increased chance of miscarriages (unfortunately, I also speak from experience of miscarriages too).
I've just checked the prices of IVF in Iran and they are SIGNIFICANTLY cheaper than in the US. To put things in perspective, the cost of one IVF cycle at the hospital/clinic I use costs around $30,000, once you factor in all the meds, appointments, procedures, etc.
So, financially, it's probably better to do IVF in Iran. You could also then get married, apply for the CR1 and then do the IVF process whilst you're waiting for the CR1 to come through. You don't need to be present for the IVF process, except for giving a sample at the clinic - which can then be frozen for when it's needed.
I know this isn't the information you've asked for - but I think it's really important that you both have this info, if you're not already aware.