My wife and I have 8 kids. The trick is to live in a low cost-of-living suburban/rural area where you can afford a 6+-bedroom house with a big yard. My wife is a SAHM so we don't have extra daycare costs. I'm a software engineer and my job pays pretty decently. We plan our budget for each month, especially for meals. Trips to Costco happen every 2 weeks.
We do okay for ourselves. No debt except for the house, which will be paid off in just a few years, after which we plan to buy a summer cabin or condo. We take plenty of trips, but usually no further than 500 miles or so, and never on a plane since airfare is too expensive.
It's just about being frugal. We have plenty of money for our needs, and have even set up college funds for each of the kids, though with the way tuition has skyrocketed and continues to do so they may need to enlist other family members' assistance when the time comes.