I kept wondering about the same question for quite a time, it makes sense to me now
It is true that He has first ionization potential (or energy) of 24.6 eV while O2 has a value of 12.6 eV for the same number. Yet experimentally igniting He discharge is much easier than igniting O2 discharge in DBD mode.
The reason in simple words is the mean free path. Think of having two identical discharges one with He as operating gas and one with O2. Assume the local electric field is identical and the gas density is identical, the mean free path of electrons in Helium is much longer than what it is in O2, which basically means that the electrons are accelerated by electric field to higher velocities (energies) in He compared to O2 before they experience a collision. So the electrons in He have larger energy than they have in O2 under similar circumstances. The difference in energy gain overcomes the difference in ionization energy.
If you wanted to test it your self, you can use a freely available software called BOLSIG+. What this software basically does is computing the electron energy distribution function (EEDF) given the cross section data of the gas (which is experimentally obtained data). For the same Electric field to gas density ratio, the mean energy of an electron in He gas is much larger than what it is in O2.
I did the following plot of mean electron energy as function of reduced electric field in both air and Helium. The reduced electric field is the electric field devided by number density. Its unit is Townsend
So for example at 300 Td, mean electron energy of an electron in helium is higher than the first ionization energy of Helium, while in air it is lower than first ionization energy of either O2 or N2.
The reason the mean free path differs significantly is that N2 and O2 are more chemically active compared to He, which means the electrons have too many possible ways of spending their energy in rotational and vibration excitation, dissociation and excitation to metastable states while in He those ways are very limited. Also it is true that the mass of a Helium atom is much smaller than the mass of O2 or N2 molecule, being the basic unit in the gas. So from a rough geometrical perspective, the He atoms are smaller in size than O2 or N2 molecules. The geometrical size is not really relevant but it helps to explain the concept.
I hope that made it clear.