Europe has in that time very clear history, so it can help us (I think) very much. First years of 16.century Europe had high economical and culture metamorphoses (Renaissance, Protestantism). Italy has been lost its advantage in trade. Genoa, who was in that time very developed town in trade by Eastern coutries divert his trade to Western and Northern Europe.
Charles V. von Habsburg bought in year 1523 Friesland, where Douw Fonda (b.1580) lived. Under his control is in that time a half of Europe. In year 1527 he occupied Italy ("sacco di Roma"). He had very high influence to link Italy with Dutch countries (Spanish route).
On the other hand in year 1562 began first revolt of Hugenots against Spanish colonisation.
I believe that Douw Fonda (and his son Jellise Douwese FONDA, who arrived to USA in year 1642) ancestors came to Friesland,Dutch from Genoa,Italy between years 1523 and 1562. I suppose, this could be his grandfather.
So in churches archives in Genoa we able to be find his family records from at least about 1500 (if exist).