Several ways to deal with this. Almost anything can be improvised to hold front wheel off the ground for removal. Big Rock, log, 2x4, metal bar et al. I used to carry an Alu Tri pod leg, no longer as I can always find something that will work.
BTW, the rear is MUCH harder to deal with.
Are you able to break the bead on your tires? ... and remount after a tube change or repair?
The front tire is usually very easy to break bead and remove tire from rim. The rear can be next to impossible without very good tools and quite a bit of experience doing it.
See Motion Pro bead breaker tools for a good one. I carry a BIG C clamp and even then it's VERY TOUGH to break the bead on my 17" rear tire.
In Mexico or Latin America I typically RIDE the tire FLAT until I find a Llantero
(tire repair shop). For under $5 USD, it's worth it to let the amigos do the job. This way can often DESTROY the tube, but I carry spares and replenish as I use them up. (not always possible, depends where you are)
I NEVER patch a tube on the road. I pull punctured tube out and replace with new, spare tube. If punctured tube is in good condition and repairable, I save it until I find a good Llantero shop and let them do a Vulcanized patch on the tube. They ALWAYS hold. Stick On patches never seem to hold long. (for me)
Some tires are so soft they won't tolerate running flat for too long and may come off the rim. Sometimes using BIG Zip Ties (Attach 4 or 5 of them) to help hold tire onto rim whilst running flat. Go slow, it works! Might be enough to get you to a repair shop.
A front tire flat usually easy to change roadside. Just swap in a NEW tube, save old tube to repair later. Keep moving, make your day's destination in daylight.