The notion of heavenly ascent by the purified is to be found in many ancient traditions of the lands adjoining the eastern part of the Mediterranean: in ancient Egyptian beliefs, in Mazdaism, in Greek and Latin philosophical traditions, in the Jewish tradition and its Christian offshoots, in Manichaeism, in Mandaeism, as well as in the Sanskrit Upanishads of India, and in the Qur'an.
In Christian writings, the ascent is by a ladder, or a series of steps, a stairway.
In the Qur'an and later Islamic writings, the ascent is by way of heavenly ropes, the asab.
Be at peace with your own soul
then heaven & earth will be at peace with you.

Enter eagerly into the treasure house
that is within you,

And you will see the things that are in heaven,
for there is but one single entry to them both.

The ladder that leads to the Kingdom
is hidden within your soul...

Dive into yourself and in your soul
and you will discover the stairs by which to ascend.

Isaac the Syrian (7th century CE)
[Jacob] dreamt that he saw a ladder, which rested on the ground with its top reaching to heaven, and angels of God were going up and down it.

Genesis 28:12
To all hastening to write their names in the book of life in the heavens, the present book is a surpassing path. Traveling by this path, we shall see that it infallibly guides those who follow its instructions, preserves them invulnerable to every obstacle and presents to us a firmly-based ladder leading us up from the earthly to the holy of holies, at the summit of which is the God of love.

John Climacus, The Ladder of Divine Ascent (6th century, CE)
When I was hard at work one day, thinking on the spiritual work needful for God's servants, four such spiritual works came to my mind, these being: reading; meditation; prayer; contemplation. This is the ladder for those in cloisters, and for others in the world who are God's Lovers, by means of which they can climb from earth to heaven. It is a marvellously tall ladder, but with just four rungs, the one end standing on the ground, the other thrilling into the clouds and showing the climber heavenly secrets.

Guigo II, A Laddere of Foure Ronges (1150)
… can you hear the wind blow, and did you know
Your stairway lies on the whispering wind.

Robert Plant, Stairway to Heaven (1971)