This question is not easy to answer. It is one of those... 'back in the mists of time' scenarios.
Robertson was born in 1815. He was an exceptional golfer – perhaps the Tiger Woods of his day. He had input into TOC, but exactly what he can be credited for is difficult to gauge. Old Daw Anderson is credited for creating the first 'double green' as late as 1832 by cutting second hole in the fifth green, but references also credit Robertson as a likely co-conspiritor.
The maps of TOC show a hole cut in the area of what we now know as the 17th green since the first plan in 1821. In those days it was called the Hole of Leslie or Bridge Hole. The green was in danger of being separated from the course when the railway was built around 1852. Since about 1870 the 'road' by the 17th green had developed. In the same year (1870) Old Tom (having been appointed as the custodian of the Links in 1865) built the new 1st green.
You could conclude that if A.R. was born in 1851, and the 1821 shows a hole cut in the area we now associate with the road hole green, then the 'green' predates A.R. And if O.T.M took over in 1865, then he is likely to have made any changes to the green when the issues with the road arose in the 1870's. e.g. the banking.
Hope that helps???
Scott
NB- From 1856 Playfair and the R&A decreed that from then forward their shall be 2 holes in every green.