What facts do you have?
Such as do you know how frequently he’s in the UK?
Do you know where the company he works for is based? (Also worth a look on LinkedIn)
Is he maybe self employed?
Does he have a lot of assets here such as property/cars? Does he rent any property?
My dh works offshore, he’s out the country more than 190 days. He pays someone to sort it all out though. He always ensures he has evidence such as boarding passes, seaman’s book etc.
Have you spoken directly to him to discuss a better private arrangement and your concerns around something not “adding up”. Perhaps a subtle mention of the implications of you asking csa for a variation based on suspicion of undeclared income and hmrc conducting an investigation may encourage him to pay for his child.
It’s definitely common offshore workers thinking they can ignore the tax rules - but there’s huge consequences when caught.
So he’s either lying and is unemployed, he is in fact working abroad but less than the 183 days and not declaring it, or he is in fact working abroad over the threshold and therefore not liable for income tax.
If he is classed as working abroad maybe this might be worth while looking into -
www.gov.uk/government/publications/countries-where-you-can-enforce-child-maintenance-decisions