The first large-scale migration of Homo sapiens that we know of was that from Africa into Europe and parts of Asia during the last glacial period around 50,000 years ago. Most of them, however, found themselves unable to cope with the harsh conditions and perished.
Others were luckier and crossed paths with Neanderthals who taught them the necessary survival skills and who were gradually assimilated into Homo sapiens, thus creating modern humans.
From Europe modern humans then migrated to Asia, Australia and back to Africa. Another migration also brought them to the Americas via the Beringia Land Bridge around 20,000 years ago.
Migration was part of life for hunter-gatherer societies, and the Neolithic Revolution some 12,000 years ago caused mass migration due to the need for farmland and the practice rapidly spreading across Europe, Asia and parts of Africa.
The hypothesised Indo-European Migrations, supported by genetic evidence, suggest mass migrations from the Ponto-Caspian Steppe into Europe, South Asia and the Middle East, beginning around 6,000 years ago and lasting for three millennia, spreading technologies like the wheel, horse domestication and chariots as well as their language.
Around the same time the Bantu Expansions took place, mass migrations originating in West-Central Africa and moving across most of the Southern part of the continent, spreading agriculture and their language.
Around 5,000 years ago people in Southeast Asia had developed sailing technologies that enabled them to travel long distances and started discovering and settling the islands of the Pacific in what is called the Austronesian Expansion.
Migration was common within the Roman Empire as well as during its decline when numerous Germanic tribes and Huns took advantage of the power vacuum by invading its former territories.
Advances in maritime navigation and the introduction of gunpowder from China paved the way for the most consequential migration wave since the out-of-Africa movement. European Christians were now able to subdue the earth by reaching all parts of the world, colonising them and enforcing white Christian supremacy while subjugating indigenous populations to their rule or annihilating them altogether like in the Americas.
This was accompanied by the kidnapping of Africans who were sold as slaves into countries ruled by white Christians. In North America the slave trade officially ended in 1808 after the US Congress passed the Act Prohibiting Importation of Slaves to boost the national slave-breeding industry, and in South America in 1831 when Brazil banned it. However, illegal trade with the Americas continued at least until 1860. With an estimated 13 million Africans abducted from their homes, the Atlantic slave trade was the world's largest forced migration before WWII.
WWII saw the greatest mass displacement in history. In Europe alone an estimated 65 million lost their homes, and while numbers for other areas are unknown, I think it is safe to say that it probably topped 100 million worldwide.
Syria was one of the many countries that gladly welcomed European refugees. However, when Syria descended into a brutal civil war seven decades later, very few Europeans reciprocated that attitude.
Jews had been disliked and persecuted for centuries, especially by white Christians since, according to their mythology, they rejected and betrayed Jesus (who, had he existed, would have been a Jew himself). Following the horrors they endured in Nazi Germany, openly discriminating against them was not an option anymore, but by giving them a country of their own, they could get rid of many if not most of them.
In WWI Great Britain had defeated the Ottoman Empire and subsequently occupied the area of Palestine which, according to Judeo-Christian mythology, their deity had promised to the Jews, so white Christian UN delegates decided to partition Palestine and give most of it to the Jews (without consulting the Palestinians, of course). The state of Israel then went on to occupy all of Palestine, establish Jewish supremacy and exterminate the indigenous population.
For better or worse, today's world has been shaped by continuous human migration, sometimes by people with inquisitive minds who wanted to expand their horizons, sometimes by people in search of farmland, sometimes by people who fled war, famine, poverty, persecution, genocide, natural disasters etc, and sometimes by people who wanted to take over others' territory and establish their ethnic and religious supremacy and who often wiped out the indigenous populations in the process.
We should keep in mind that all of us are either migrants or descendants of migrants (except for anyone who lives in the Makgadikgadi Basin and whose ancestors never left the area) and accept that migration will always be part of humanity.