Sayyiduna Abu Hurairah (may Allah be pleased with him) narrates that when the Messenger of Allah (peace and blessings be upon him) said « اللهُأَكْبَرُ » at the beginning of the prayer, he would remain silent for a short while. So I asked, "O Messenger of Allah (peace and blessings be upon him), may my parents be sacrificed for you, please tell me what you recite in your silence between the takbeer and the recitation?" The Prophet (peace and blessings be upon him) replied: "I recite this supplication « اللّٰهُمَّبَاعِدْبَيْنِيوَبَيْنَخَطَايَايَكَمَابَاعَدْتَبَيْنَالْمَشْرِقِوَالْمَغْرِبِ،اللّٰهُمَّنَقِّنِيمِنْخَطَايَايَكَمَايُنَقَّىالثَّوْبُالْأَبْيَضُمِنَالدَّنَسِ،اللّٰهُمَّاغْسِلْنِيمِنْخَطَايَايَبِالثَّلْجِوَالْمَاءِوَالْبَرَدِ » 'O Allah, distance me from my sins as You have distanced the East from the West. O Allah, purify me of my sins as a white garment is purified of dirt. O Allah, wash away my sins with water, snow, and hail.'"
The evidence for this is that (supplication) in the opening is among the differences that are permissible, and it is allowed for the one praying to begin the prayer with (any supplication) that is proven from the Prophet ﷺ that he used to begin the prayer with after the takbeer, whether it is with the praise and glorification of Allah Almighty, or those supplications that are mentioned in the Qur'an, or those supplications that are not mentioned in the Qur'an.