Approaching 0.042% -
Keep in mind that there is ~10 - 15km of atmosphere before outward travelling IR escapes to space - plenty of opportunity for such concentrations of CO2 to absorb IR (to re-radiate in all directions, ie as much down as up... almost the textbook definition of Greenhouse Effect) and enough to prevent most IR from the ground getting to space in one go, even before concentrations were raised.
"Only" 0.04% is a very misleading description; very small relative to what? The earliest calculation of the greenhouse effect from lowered and raised CO2, by Svante Arrhenius was in the 1890's, following on from prior work of others that reconciled known incoming solar energy with global average temperatures much higher than could be explained in an absence of greenhouse effect; it is highly significant, even at lower concentrations than 0.04%.
And even if CO2 greenhouse contribution to the total GHE is not the largest - 2nd after water vapor - it is what we are changing by fossil fuel burning. With (as previously mentioned) water vapor concentrations changing in response to the warming from other GHG's and amplifying the effect.