This is a long shot, since the Big Crunch and Big Bang aren't explicitly described, but the storyline implies it. (You probably know by now the trope is fairly common.)
The Time Decelerator (A. McFadyen, Jr.) describe two scientists, Kirschner and Latimer, who develop a time machine that works on pure handwavium:
In June he said, “The discovery, by mass spectrum analysis, that mass was a function of motion, upset the classical dictum that gravitation was a function of mass. And the view of Einstein and others that distances varied with the velocity of the observer similiarly threw light on the previously unquestioned principle that gravitation varied inversely as the square of the distance.
“From these premises Einstein made the deduction that motion and gravitation are exactly and ultimately equivalent, that the phenomena each give rise to are wholly identical. Consequently, time is a function, not only of motion, but of gravitation also, and the speed of a chemical reaction, for instance, varies inversely as the intensity of the gravitational field in which the reaction takes place. Johnny, do you remember what I said months ago? Then, under the influence of a suitable gravity field, a man would never die ”
In January, 1936, he said, “The control must be independent of the G-field, or it will be subject to the lengthening of the time interval also. You’d go up, Johnny, and never come down. What’s the answer?”
Sure enough, an intended 15-minute trip turns out to be 4 years, then 40, then 400; at that time they understand the effect better, but are unaware of his machine.
“Four forty-four!” the girl exclaimed. “1936 But that’s impossible, you must be mistaken. The curve field wasn’t developed until 2060, and the field machine is even more recent — 2210, I think. It’s impossible.”
“That machine,” he said firmly, pointing to it, “was developed in 1936, by Dr. George Kirschner and Dr. Johnny Latimer. I am Latimer, and I have come in it against my will. If this is 2380 I have skipped four hundred and fortyfour years, and I would like to get back if only to find out what happened to Kirschner, who was a friend of mine.”
“You can’t go back.” Slowly she shook her head. “The curve field operates in one direction only, as you probably know. The interval can be lengthened, but it cannot be shortened or reversed. We have had it for a hundred and seventy years, but few have ever dared to skip more than a dozen years, or less, for it is difficult to control at higher velocities. What are you going to do?”
Here the story sounds like a synopsis of your post. He accidentally activates the machine one more time, and appears to complete the loop, returning to the place of the original experiment 40 minutes after leaving.
Too late!
As he half crouched there on the roof, fighting to get up and away from the machine, there was a gigantic tugging at his body, and instantly it seemed to snatch him back on the framework of that strange device. Then darkness closed in, and even the roaring voice was stilled
HE RETURNED to consciousness as he had done before, but slowly and familiarly now. His eyes pierced a lifting, thinning darkness, and saw that his body was sprawled half out of the seat of the machine, and that there was a well-known scene around him. The last wisps cleared, and he was able to look over the edge of the machine, down through a hundred feet of air and sunshine, and see the foreshortened figure of Dr. George Kirschner, staring up at him.