Increasing stamina does always take time!
I used to hate running and still do mostly, but I started with sessions on the recumbant stationary bike, then started treadmill walking and jogging and actually got to really like treadmill running. I kind of made up my own interval thing, with walking and running. I don't do it these days cuz I can't afford a gym but i tried running outside and it's just not for my knees...and the monitoring of progress on the treadmill is nice, right in front of you with the distance readout.
You can also try interval training with many cardio exercises. I downloaded an interval timer and I do 20 secs of jump rope 10 secs of rest and repeat that 8 times, take one minute rest, and do it again.
You can do that kind of thing for any intense exercise that would b rly tough to just do for ten minutes straight: burpees, jumping jacks, mountain climbers. Heck, mix it up. Anything that gets you breathing hard, do it hard in intervals.