I started north of 317 (my highest recorded weight, but I know I was over that) on a 1990s steel MTB. I didn't have a way to track my first rides but they were probably in the 5 mile range on flat ground through quiet residential streets. I can remember coming into the house, flopping on the couch and moaning.
At about two months I did my first "destination" ride to a neighboring town about 9 miles away. I rested at the turn around and a couple of times on the way home but made it OK.
By mid-summer I was doing 15 mile no-drop rides with the club from an area bike shop. I got seriously hooked and upgraded to an entry level used road bike.
In June the following summer (about 14 months of riding with a couple off during mid-winter) I did my first century for the American Diabetes Association Tour de Cure. Later that summer I did another century at the Headwaters 100 in hilly lakes country.
I'm still comfortably into Clyde territory and ride 20-50 miles two to three times a week with some family riding, commuting and errands by bike in-between. I haven't done a century this year but I hope to get a couple in before the snow flies.
Stick with it and don't compare yourself to others. Set realistic short-term goals and keep it challenging but enjoyable.