Is it permissible to falsify a certificate to obtain a job that helps support the family and pay off debts, knowing that there are pressures and difficult circumstances?

Falsifying academic certificates and obtaining them is unlawful (haram (definition)). The fundamental principle is that what the questioner mentioned does not fall under the necessities that permit prohibitions. Necessity (ḍarūrah) is when a person reaches a point where, if they do not partake of the forbidden, they will perish or be on the verge of perishing. The mufti (definition) does not see any aspect of necessity in the questioner's story, as he can work and earn a living in fields that do not require a certificate. Therefore, there is no necessity in his case that would compel him to commit what is prohibited.