Sources say English was rhotic in most places in the 17th century. How do they know that? Obviously, we don't have any samples of recorded speech from that time.
In addition to rhymes and dictionaries already noted, you can cite spelling shifts in which the "r" letter positioned after a vowel disappears from certain words.
The Wikipedia article about Rhotic and non-rhotic accents cites
the Oxford English Dictionary reports bace for earlier barse (today "bass", the fish) in 1440 and passel for parcel in 1468.
which is more or less the time frame in the question. This shows, assuming the spelling evolution follows the pronunciation shift, that in this words the rhotic pronunciation had disappeared as well.
Also have a look to a contemporary phenomenon named "The Great vowel shift".
For one thing, there are dictionaries from that time that indicate pronunciation, and we can learn from how they write down pronunciation. For example, I have heard Walker's Critical Pronouncing Dictionary cited as a source on that matter.
Well for one thing if it wasn't people would not write it down(but then again that's not always true because of influence from other language orthography)second the english left in the US that was left far before the one in australia has the r in many of it's variants and most importantly people wrote that the r sound was pronounced in pronunciation books or else when describing the way someone speaks also some extremists in the high classes in britian wanted the king to ban the dropping of r when it started picking up in their circle groups showing that it was pronounced ,definitely in some people!