Lots of interesting notes in this thread, so I'll throw in my 3 ha'p'orth of comments in the form of my own experience in case it helps.
The basis of my comments are from being a non-athletic person, a person who dislikes physical exercise for the sake of it, who never runs, and who hasn't been in a gym since leaving school.
Jumping back to when I was aged about 30, when my only normal physical exercise was commuting about 2.5 miles each way to/from work in the middle of Newcastle upon Tyne (overall downhill to work, uphill going home), plus walking maybe a mile or so most lunchtimes: One sunny spring day I decided to go out for a cycle ride for the day. No planning, just picked up a map and puncture repair kit and a jumper and set off at maybe 9-10 am. No breakfast first, as I did not normally do breakfast. No lycra, no cycling shorts, just jeans and T-shirt. In those days I didn't even have a helmet. I cycled out to the coast and then northwards, stopped at a pub at lunchtime and had a couple of pints of nice ale and a toasted cheese and onion sandwich then carried on, once or twice stopping to admire the surroundings. Got to Alnwick, watched a bit of a medieval fayre for an hour or so then decided it was time to head home. As I was approaching Morpeth, after about 55 miles, I was really struggling, the last few miles having been hard work, and I was seriously doubting I could make the remaining 15-20 miles home, and so decided to head into Morpeth itself to get the train back. As I pulled off the A1 there was a petrol station, and I realised I was hungry and thirsty. I stopped and had a Coke and two Mars bars. Then got on my bike and cycled home. Being unaccustomed I had simply not considered the energy needed to cycle that distance, and had run out -a top up of sugar and I was on my way, and that is the moral of this particular story. No adverse effects the next day, despite having cycled about 75 miles with no prior training (and no padded shorts), though overall that area is not excessively hilly.
About three months later a friend of mine was doing a John O'Groats to Lands End charity ride, and I joined her for a day in the Lake District, meeting up at Brampton near Carlisle first thing, and I rode to Kendal, then train to Carlisle and cycled back to my car in Brampton -about 70 miles total. That day I did have breakfast before setting off, and we stopped for lunch in Appleby-in-Wetmoreland (no S because it didn't deserve it!). Much hillier terrain than my previous long ride, and I well remember the long haul up out of Appleby, having to weave from side to side as I strained to progress on my aging 5-speed road bike - while someone on a MTB pootled along nonchalently in bottom gear with legs moving faster than I can move mine at the best of times! Again, no after effects the next day despite again no preparation. The moral of this story is get a bike with lots of gears ( I soon bought a simple MTB bike and equipped it with road tyres, and more recently a road bike with the widest gear range of anything I could find, almost as low as a MTB and almost as high as a racing bike, so I can cope with most things a road throws at me. It is worth noting that my friend and her companions, doing typically at least 70-100 miles a day, were eating 3 big meals every day - and the consequence of that was apparently a struggle to reduce to normal eating afterwards -but that a was 1000 or so miles in total!
Clearly the fitter you are the easier it will be, and very likely the younger you are that might apply all the more - I might struggle more if I were to attempt today than 30 years ago - but I would happily attempt it, with my only preparation maybe a few more miles than my normal commute - someone's suggestion
On those two rides my bike had wire toe baskets, but they were deep enough for me to be able to pull as well as push - though I'm not sure that I pulled anywhere as near as much ad I pushed! And the bike, a cheap 1970s 5-speed drop-bar road bike was scarcely light or sophisticated like many today, so if you have something lighter, so much the better.
In case of rain, do take something truly waterproof to keep things like phone and anything else easily harmed by water - can be as simple as a knotted or clip-top plastic bag.