Say if someone has work or school on Friday, they have no time to perform ghusl for the Jumu'ah prayer.
Can they do ghusl after Maghrib on Thursday since the day begins at night in Islam? (Hanafi view)
Theoretically after the maghrib the day starts so this time would be counted as part of the Friday (from this point of view).
As I in first place over read the restriction on the hanafi view my answer is more general, but addressing the two main positions in the hanafi madhhab in particular, hoping it would be helpful for others.
The major differences between scholars
The scholars held different opinion about when the ghusl for jmu'ah has to be performed to be valid and counted as such. The major difference is whether they consider the ghusl as relevant for the prayer or the day!
Some of them say it only counts as ghusl for jumu'ah if it was done right before leaving for the prayer (for example imam Malik held this position and al-Bahuti -hanbali- considers it as the most recommended way).
A majority of scholars (Shafi'i, Hanbali and Dhahiri school of fiqh and scholars such al-Hassan al-Basri, Ibraheem an-Nakha'i, Sufyan at-Thawri, Mujahid, abu Thawr and Ishaaq ibn Rahawayh) say it only counts after the true fajr (al-fajr as-Saadiq) as this is what was done by the sahaba and seems to be the conclusion of the ahadith such as:
He who takes a bath on Friday, the bath which is obligatory after the sexual discharge and then goes (to the mosque), he is like one who offers a she-camel as a sacrifice, and he who comes at the second hour would be like one who offers a cow, and he who comes at the third hour is live one who offers a ram with horns, and he who comes at the fourth hour is like one who offers a hen, and he who comes at the fifth hour is like one who offers an egg. And when the Imam comes out, the angels are also present and listen to the mention of God (the sermon). (See for example in sahih Muslim)
I've pointed at the difference of opinion about the interpretation of this hadith in my answer on What is the reasoning behind the opinion of jumaah before dhuhr?.
Among those who allow performing this ghusl before the fajr you may find al-Imam al-Awaza'i and maybe this is a second but not strong view in the shafi'i school of fiqh as al-Khateeb a-Shirbini says "it was also said it is allowed after the middle of the night." after quoting the dominant view.
The discussion inside the hanafi madhhab
Now let's address you inquiry about the hanafi madhhab:
Abu Yusuf held the opinion that it can be performed before fajr and it can be done before the prayer as long as one keeps his taharah! Else he won't be rewarded for the ghusl of jumu'ah unless he repeats the ghusl. So he considers the ghusl as a ghusl for the jumu'ah prayer to some extent similar to the majority of scholars.
But the main view of the hanafi school of fiqh and that of Muhamamd ibn al-Hassan is that the ghusl is for the day of jumu'ah so whenever one performs it between fajr and maghrib it is valid as there are ahadith allowing to pray jumu'ah with wudu' only (see for example in bada'i as-Sna'i of al-Kasani or in Fath al-Qadir of ibn al-Humam).
This is also the view of ibn Hazm they consider the gusl as related to the day not the prayer of jumu'ah!
Some sources other: