Yes, we all managed to learn to hold up our heads before Tummy time was invented.
Tummy time is more about protecting the head shape, as several fairly recent changes to the way babies spend their time is causing flathead to become very common. The "back to sleep campaign" combined with the effects of babies spending time in car-seat, pushchairs and bouncy seats, mean that babies can be spending almost all their time with the back of the head compressed against a solid surface (this doesn't happen when baby is carried, or lies on it's tummy). a baby skull is so soft that they deform very quickly for the first few months.
My DH is a GP and has been advising people about this for some time, and when our own DS4 (now 9months) was about 7 or 8 weeks old we could already see considerable flattening, with bulging to one side of the head (as he always turned his head a little to the other side when sleeping). We had already bought an expensive mattress for his cot (or we would have got one of the special mattresses that are available with a groove in them for the head to lie in, to prevent/cure flathead), so we opted for a cheaper alternative (£12 I think) of a "butterfly" infant pillow for flathead prevention, no doubt HV will be saying "baby pillows are not safe", but this is, and is designed for use from birth.
After 2 weeks of use, there was already a visible change to DS4 head shape (less flat), and the bulge took longer, but has now almost equalized with the other side of the head. Time is of the essence, by the time a child is 18 months/2 years, it is very difficult to influence the shape of the head as the bones are thicker and less flexible.
None of my (now teenage) DS 1-3 have any particular flattening, and no bulges as it was still "sleep on their sides" in those days (alternate sides each time they went down to sleep), as far as I can remember.