Well there was a collapse, but it "only" lasted for 100 to 200 years and no anything close to 600. Populations in Mediterranean and European decreased sharply between 5th and 6th centuries due to the plague and climate change and growth remained modest until the medieval warm period. However there was nothing the people living at the time could have realistically done to avoid this.

However outside of that period it's not that straightforward. The Roman economy was stagnant or declining well before the Western empire officially collapsed. According to some historians growth in much of the Mediterranean region stopped with the Roman conquests at the end of the Hellenistic period. But even if we assume that ~200 A.D. was the peak can we really say that there was more technological innovation and economic growth between the 3rd - 5th centuries than between the 8th and 10th centuries? Probably the latter..

And it also varied significantly depending on the area we're talking about. Italy probably took the longest to recover but it's economy was massively inflated due to wealth transfers during the Roman period. However the center of economic and political power in Europe has shifted to the other side of the alps France and Germany had nearly the double the population in 1000 AD compared to their Roman peaks. And some places like mainland Greece arguably never did until the 19th century (it was probably was past it's peak during the Roman period as well, though. A similar process occurred in the eastern Mediterranean where the center of power shifted from the coast to the inland areas (like the area modern day Iraq).

And we're only taking about absolute growth here, per capita productivity probably wasn't as much affected and most of the decline in international trade (which eventually recovered) was balanced out by higher availability of land (per capita) and improvements in agricultural techniques and tools.

If we're talking about technological growth, well again in some areas like architecture the decline was severe and near total (most communities couldn't afford to maintain the buildings they already had). In other areas the reverse might had happened, based on archeological evidence the average quality of metal tools and weapons in Western Europe was already much better in the 7-8th centuries compared to what the Romans ever had. The heavy plow was introduced in agriculture, water mills continued to be built. Literacy rates fell, however that was to a large degree an outcome of the collapse of urban populations. However the link between economic and technological progress and education in the ancient world wasn't all that clear.