Hi,
I just had my first baby 2 days before my 38th birthday. It took us three years and a lot of heartache, but we have a healthy beautiful daughter.
My opinion is to decide how much of a priority this is for you. If it is number one, then who needs a marriage certificate to start trying? (if you and your boyfriend are both really ready) Three of my friends who are my age or older did the pregnant while engaged thing because you never know how long it will take and planning a wedding can be stressful so they dealt with one thing at a time.
Also, I understand that you want to avoid fertility treatments, but there is a wide range of tests and treatments. Even if I didn't want to do fertility treatments (we did end up having to use IVF to have a viable pregnancy) I would recommend going to a specialist after 6 months of trying just to get a few tests done. There are some conditions that are treatable (and some that aren't) that can effect your fertility. If you should happen to find out that you can't get pregnant without assistance then you can make some informed choices (treatment, adoption etc). Personally I feel like it would be devastating to try on your own for a long time, then decide to get tests only to find out that you weren't able to get pregnant on your own - especially at this age. Although most infertility unexplained.
If you decide that having children is something you would like, but only if it happens totally on your own then just make sure your prenatal has lots of folic acid and limit your caffeine and alcohol. Have your partner avoid hot baths, hot tubs, heated seats, and limit alcohol etc for a few months before you start trying.
You will also need to discuss this with your boyfriend. Are you going to just casually try for a few months (meaning not tracking your ovulation, temp, blah blah blah) or are you going to get serious about it right away. You will hear of people who get pregnant on their first try (or without trying) and they are super fortunate, but I think there are a lot more people out there (especially those of us who are AMA Advanced Maternal Age -yuck!) who had trouble. My husband and I had different opinions on this. He was looking forward to the "Trying" and I was just feeling the clock ticking and wanted to get serious about timing and tracking.
So anyway, at some point have an open discussion about expectations etc with your boyfriend.
I wish you the best of luck, try to avoid stress, and I hope you have a healthy baby soon.
D.