Does the intention to wake up justify a young man staying up all night and missing the Dhuhr and Asr prayers, knowing how difficult it is for him to wake up, and can the Hadith "The pen is lifted from three... and from the sleeper until he awakens" be used as an argument in such a case?

A Muslim must perform the obligatory prayers at their prescribed times, as Allah the Almighty says: "Indeed, prayer has been decreed upon the believers a time-bound ordinance," and the Prophet, peace and blessings be upon him, said: "Five prayers Allah عز وجل has made obligatory. Whoever performs ablution for them well, prays them at their due times, completes their bowing, prostration, and humility, will have a covenant with Allah that He will forgive him. And whoever does not do so, has no covenant with Allah; if He wills, He may forgive him, and if He wills, He may punish him." Staying up late after 'Isha prayer is disliked, and if staying up late leads to missing prayers, then it is forbidden. The narration about the pen being lifted from the sleeper is not an excuse for staying up late such that it leads to missing prayers.