The short answer is simply; we don't know. Also, apologies for the following formatting, because I'm on mobile.

The Picts only really first show up towards late antiquity, when a confederation of Picts was formed, possibly in response to the Roman Empire on their southern borders. The first use of "Pict" as a name for these people occurs in a panegyric from the very late 3rd century, and is usually held to mean "the painted people".

The Pictish Chronicle, a pseudo-historical account of the Pictish kings dated to around the 10th century, presents the Picts as conquerors from Scythia, as does the Anglo-Saxon Chronicle, Bede's Ecclesiastical History, and Geoffrey of Monmouth's History of the Kings of Britain, though considering how much these sources would have borrowed from one another this view isn't generally regarded as accurate by most historians of the era. If, however, the Picts were indeed descended from Scythia, that would put them around central Asia, near Kazakhstan or thereabouts.

It's generally assumed that the Picts were simply descendants of the Caledonians, or some of the other tribes that occupied Alba in earlier centuries that are mentioned by numerous Roman geographers as well as on Ptolemy's world map. The Caledonians were themselves Celtic, with likely origins being in western or central Europe, and are first attested iirc by Tacitus in his Agricola. As we don't really know what the Picts called themselves, it's entirely possible that they even called themselves Caledonians or continued the use of another Iron Age Celtic tribal name; it's been suggested that they called themselves the Albidosi, based on the name found in the Chronicle of the Kings of Alba during the reign of Malcolm I, but even that's disputed by some historians. Really we just don't know much for certain.

There's very little in the way of surviving Pictish writing to tell us much about their language or history in their own words, so we have to rely on what we know of them from folks like Bede and the Irish annals, as well as the scant archaeology that we have that's "distinctly" Pictish.

Sources:

Bede, Ecclesiastical History of the English People.

Geoffrey of Monmouth, History of the Kings of Britain.

Broun, D. 2005, 'Alba: Pictish Homeland or Irish Offshoot?', in P. O'Neill ed., Exile and Homecoming: Papers from the Fifth Australian Conference of Celtic Studies, University of Sydney, July 2004. Sydney: University of Sydney Press, 234-275.

Fraser, J. E. 2011, 'From Ancient Scythia to The Problem of the Picts: Thoughts on the Quest for Pictish Origins', in S. T. Driscoll et al eds., Pictish Progress: New Studies on Northern Britain in the Early Middle Ages. Leiden: Brill, 15-44.

Woolf, A. 2007, From Pictland to Alba 789 - 1070. Edinburgh: Edinburgh University Press.