Yes, Allah can definitely pay your debts. He can do anything. You only need to trust him.
So long as you have taken on a debt so that you can fulfill the duty of helping your family to pay for living expenses, you will be rewarded by Allah for this good deed and he will help you to pay off this debt. He will open a way out and don't forget where there is a will, Allah can create a way.
Our prophet says: , “The one who takes people’s wealth intending to pay it back, Allah will pay it back for him, and the one who takes it intending to destroy it, Allah will destroy him.” (Al-Bukhari 2387)
All you need to do is surrender your debt, your doubts and fears, your life and affairs, your business, your family affairs, your finances to him and pray to him to pay your debts. He is even now doing it, as it is his desire to free you from every burden. You should strive hard and face every disturbing thought, such as “I can’t,” “I don’t know how,” “I can’t see the way,” with the affirmation that allah will help me. New ideas will speed up in your mind and you can use them to start this very moment to pay your debts. You should begin by thanking Allah for your freedom from the debt-burden thought. This is an important step in reducing your debt. The funds to pay all your bills may not suddenly appear in a lump sum; but as you watch and work and pray, holding yourself in the consciousness of Allah’s leadership you will notice your funds beginning to grow “here a little, there a little,” and increasing more and more rapidly as your faith increases and your anxious thoughts are calmed. With this increase you will gain good judgment and wisdom in the management of your affairs and debt will soon disappear when wisdom and good judgment are in control.
Your desire to be free, with the realization that debt has no legitimate place in Allah’s empire and your determination to erase it entirely is the way only to be free from debt.
Work toward this freedom and continue with your meditation and prayer. Do not concentrate on debts or spoil your prayers by constantly thinking of debts. Think of that which you want to prove, not that from which you seek freedom. When you pray, thank Allah for His care and guidance, for his provision, for his love and wisdom, for his countless blessings and your opportunity to enjoy it.
May allah make us burden free and give us guidance in everything. ameen