A low oil level cannot trigger the check engine light to come on because the computer that turns the check engine light on cannot detect the low oil level unless your vehicle has a low oil level light.
Most commonly when a check engine light comes on it can be a loose or bad gas cap, engine misfire due to bad spark plugs, bad ignition coils, bad spark plugs, bad ignition module etc.
Either way if the check engine light is coming on there is a problem somewhere that needs fixed and you can take your vehicle to an auto parts store such as Autozone for a free check engine light test.
They will plug a tool into your vehicle and pull up codes that tells exactly what is going on with your vehicle to cause the check engine light to come on.
Sometimes it's as simple as a loose gas cap or faulty gas cap causing the check engine light to come on.
If your car has a low oil oil or an oil light that comes on then that could mean your engine oil level is low or the oil needs changed.