Is the husband considered sinful for delaying procreation due to his inability to afford the costs of medical examinations and childbirth, despite his certainty that sustenance comes from Allah?

It is not permissible to prevent pregnancy for fear of poverty or for other reasons not deemed valid by Islamic law, because Allah is the Provider and has guaranteed the provision of every creature. The Quran has prohibited killing children, whether poverty is present or anticipated, and procreation is among the means of sustenance. A Muslim must trust in their Lord and rely upon Him.