I have compiled such a timetable for a location close to Switzerland and formerly belonging to St.Gallen (now Switzerland): Rothenfels, a once independent small territory near todays Immenstadt.

Of course we know of the Romans who invaded BC and stayed until the 5th century. Before the Romans is what we wouldn't call an Empire because the Celts and Rhaeter didn't bother to form big structures, similar to France and southern Germany. So before Rome we had ~400 years of La Tene, 300 years of Hallstadt, both Celtic iron age cultures. The bronce age from 1700BC to abt 700BC certainly had important settlements we don't know much of because they were scriptless. First human settlements in more alpine regions date from the bronce age. Stone age before (after 5500BC) preferred easy farmable regions. Occasional pre-neolithic remains can be found all over the alps too.

After Rome it developed quite interesting. The Alamanni who raided through the region down to Italy in the 260s and who are the genetic forbearers of todays Swiss (and Vorarlberg and Allgäu people) stayed after about 470 permanently.

After 493, when Theoderich came to power we became part of his Visigothic Kingdom. At some time around 500 the Byzantines stroke back and possibly for a short time parts of Switzerland were even part of eastern Rome (Byzantine Empire).

After 536 Witichus (Visigothic) gave big parts, including Bodensee area to the Francs who took over (always opposing the Alamanni).

In the 6th to 8th century the Alamanni managed to become locally a little independent (under the Francs), more and more incorporated into the Francs Reich. Which split up after Charlemagne, Switzerland was within the HRR (HRE) then. Quite independent areas, overruled by an emperor.

The Swiss areas (and others too) gained more and more independence from the emperor over the centuries. Most Swiss prefer to hear 1291 as the real date of independence (similar to Rothenfels which was bought 1243 by Emperor Friedrich II-stupor mundi- to be owned by himself). Other possibilities to mention would be in the 1500s. In the year 1648 (Peace_of_Westphalia) the Swiss cantons left the HRE officially and thus were independent.

Switzerland was inhabited by a group known as the La Tène culture after an archaeological site on the Neuenburgersee where their artifacts were first discovered. Despite the name, the La Tène people seem to have been concentrated in the Paris basin and the mid-Rhine, but they were certainly present in Switzerland for a long time. Some have classified the La Tène as a Celtic culture, and Greek and Roman sources called them this, but it's possible they may not have seen themselves this way.