There is a ton of debt, but on the flipside most specialties (orthopedic surgery for sure) have high enough salaries out of residency that handling the payments is very feasible. Federal loans don't require payments unless you're attending less than half-time so it's not like you'd be in school and trying to make payments at the same time (I don't know what the deal is for private loans).
It is a stress for sure, but at least it isn't comparable to, say, getting your PhD in Art History and trying to to pay off $150K in loans on the $30K/year you have once out (sorry, art history people . . .). There is totally room for starting a family when you have that debt load when you have the income to compensate.
The big caveat: those families are being started once they get those big salaries, or in residency.
Regarding time commitment, undergrad and med school are very different. With many colleges you could work and then go to school part-time to finish your undergrad degree. Aside from increased time to completion, it doesn't leave you a lot of time to help with child care, and going part-time would render you ineligible for many financial aid programs. But it is totally possible, many parents do it, and it's worth it as an unfortunate truth of the workplace is a college degree is a prerequisite for most jobs that provide a living wage (outside of construction, electricians, plumbing, trade school positions, etc).
But no med school I know of allows for part-time attendance. Hopefully at that point your girlfriend could provide the financial support while you are in school full-time. If you take, say, 7-8 years to finish undergrad then your kid would be in first grade and at least you guys wouldn't have to worry about daycare. Med school would be an income dead zone unless you find odd jobs, but once you get to residencies you start earning a small income again. Or you could look at shorter healthcare professional programs, like a DPT or NP, which would involve less debt load and total time commitment while still providing a good salary and job prospects once you're out.
You could also consider just putting your plans on hold completely until your kid is old enough to be in school, and then go from there.
I dunno if this is out of the purview of this subreddit or not, but if I were you my bigger concerns would be relational, not financial. No matter what happens in the future between you and your lady once you have a child together you two will be linked for the rest of the child's life. So achieving your goals is possible but it will require a lot of communication and compromise, and you and your girlfriend will need to be on the same page every step of the way.
For example, outside of heavy familial support it would likely not be possible for both of you to pursue school at the same time, so if she has career aspirations too you would need to hash that out. The partner who is not attending school while working is basically signing off on being the primary caretaker until the other person graduates. That is a really, really tough position to be in, especially when the kid is young and cannot go to public school yet.
I think as you guys are having conversations about this your concerns should not only be "Can we pay for this?" but "How does this fit into our life goals? How will we each compromise on our goals to help the other succeed? How will we specifically be splitting child-care duties, like getting up when the child needs to be fed at 2am and staying home from work if the child is sick?" And you're going to have these conversations multiple times throughout the course of the child's life, because as your feelings and the situation changes you will have to adapt your decisions. Ultimately the results of those conversations will have more of an impact on your aspirations than debt load.