My '70-C does that sometimes, but only when it's cold. If I run the oil pan heat for 30-45 minutes if the temps are around freezing, or 1 hr or so if in the 20's, I have few problems.
Something I learned at the MAPA PPP is to run the electric fuel pump only until the fuel pressure maxes out, then turn if off. Next, push the mixture to rich, and pump the throttle several times [twice if temps are comfortable, 3-4 if cold, and 5 or 6 times if very far below freezing] and sit there for a minute while the fuel vaporizes before cranking. If all else fails, pull it into a heated hangar for 30-45 minutes while freshening the battery.
If you want to recharge your battery without removing the top cowl, I find a half hour or so at 2400 or 2500 RPMs works really well, and I get to sightsee at the same time. There's no need for high power [20" or 21" should do the job], but you'll still cover a lot of ground. Practice some maneuvers, timed turns, do an approach or two, and the battery should be pretty well charged, assuming it starts in the first place.
Again, this is only a problem in the winter, and bit me in my 4th month of ownership. Since then, I've only had two times it wouldn't crank--once when heat wasn't available, and last week when the temps were in the teens and the oil preheat had been plugged in overnight. Never did figure that one out, but charged the battery and it fired right up the next day. My coldest departure was 8F, with overnight oil preheat, and hand-turning the prop 3-4 revolutions immediately before boarding, and it cranked just fine.
Good luck with yours. Sometimes it's a challenge to find enough cockpit duties to kill 60 seconds between pumping throttle and cranking. Winding and setting the clock just doesn't take long enough. Sometimes I just wish it had a priming function!
--Hank