Paul does not say 'how', only 'that'. It did happen, to him, this 'separating' and this 'calling'. But when he goes on to say 'why', then the matter of God's sovereign, predestining arises for consideration.
This is what Paul said in Galatians 1:15-16
"...and when God was well pleased - having separated me from the womb
of my mother, and having called [me] through His grace - to reveal His
Son in me, that I might proclaim Him good news among the nations,
immediately I conferred not with flesh and blood." - Y.L.T.
This indicates that God was well pleased at his separating Paul from his mother's womb. God was separating him for a purpose. In his gracious providence, God had ensured this baby was conceived - not by chance, or by a father's will - and prospered sufficiently in the womb to arrive at that point of separation - birth. God ensured the birth was successful. God ensured the baby grew to a young man who was well educated as a Roman citizen, being a linguist also deeply versed in the ancient Hebrew scriptures and ways of the Judaic religion. God knew before Paul was conceived that he would grow to learn at the feet of Gamaliel, a Pharisee of high renown (Acts 5:34 & 22:3). God also knew in the counsel of his will that Paul would witness the stoning of Stephen to death, and go on himself to wickedly persecute and imprison Christians, such was his hatred against Christ and his followers. But God knew why this young man arrived at that point, and at what precise point in time during that tirade that the risen Christ should break through into his life.
Now, when Paul wrote those words in his letter to Galatian Christians, he could look back with hindsight and see the hand of God traced in all of that, but he still could not say 'how' God did that; only that he did. He must have reflected on the wonder of God's grace in allowing him to be born, despite what he would grow up to do (based on his beliefs). He came to realise that God had a purpose, and that God was calling him to be an apostle to the nations - the Gentiles. Paul became aware of that calling after his conversion to faith in Christ, but is it not the case that God's whole plan, calling and will for Paul, had been worked out in the counsels of eternity, before any creation started?
After all, God does not have Plan A, with another Plan B in reserve, in case anything goes wrong with the first one. The Almighty is sovereign over everything and everyone. Whether we like that idea or not, the scriptures show this, and Paul spoke of God's eternal plan in connection with himself (and this is the closest we can get to learning how God did this). Paul speaks of the hidden mystery of God, in Christ, not revealed in previous ages, but now revealed to the prophets and apostles:
"...whereof I was made a minister, according to the gift of the grace
of God given unto me by the effectual working of his power. ...And to
make all men see what is the fellowship of the mystery, which from the
beginning of the world hath been hid in God, who created all things by
Jesus Christ: To the intent that now unto the principalities and
powers in heavenly places might be made known by the church the
manifold wisdom of God, according to the eternal purpose which he
purposed in Christ Jesus our Lord." Ephesians 3:5-11 A.V. (Bold mine)
The purpose (plan) to ensure a baby would be safely born on earth to grow to the manhood of Jesus Christ, to suffer, die and be resurrected, had all been worked out in the counsels of eternity, before any creating started. Likewise, the purpose (plan) to ensure another baby would be safely born on earth to grow to the manhood of Saul of Tarsus, who would then become God's evangelistic minister of the good news of Christ to the Gentiles, had all been worked out in the counsels of eternity, before any creating started.
It is illogical to think otherwise, because God had to know every last detail of every person created, then born on earth, and all circumstances pertaining to them, to ensure the fulfilment of his promise for "the seed of the woman" to culminate in baby Jesus, and for another baby to then become Jesus Christ's minister to the Gentiles.
The nearest Paul (and we ourselves) can get to knowing "how God separated him from his mother's womb", is what Paul said there in Ephesians. But what he said there shows the 'why' - the eternal plan, the mystery gradually revealed to humanity, requiring a man like Paul to play a part in revealing this mystery to the Gentiles. That is how to understand "the separation".