According to the standard textbook, "Album Renault 4" by Robert Séjourné (I wonder if he is any relation of the man who built the famous Séjourné Viaduct on the Pyrenean Ligne Jaune?), the first versions of the R4 were introduced in August 1961. The first version was the 4L and this had a tailgate which hinged upwards, as on later vehicles.
The hinged-down tailgate, illustrated on page 43, seems to have been specific to the R4 Super (or Super Confort) which was introduced in March 1962 and discontinued on 24th September 1962 after 7216 had been built. It was given its own type number, R1122. Interestingly, although the engine was the same (747cc) as the other R4s the book states that it was beefed-up as regards horsepower, 32HP as opposed to 26.5 : apparently via bigger valve inlets (see p. 67).
The R1122 was replaced by the R1124 R4 Super, which had the 845cc engine. It also had the hinged-down tailgate. In December 1963 this tailgate was discontinued in favour of the "ordinary" pattern. In December 1964 the R1124 was discontinued although the "Super" name remained attached to some R1123 models.
So the way to date your vehicle is : if it is R1122, then 3/62 to 9/62. If R1124 then 9/62 to 12/63 given the tailgate pattern.
If you can get hold of copies of the first two R4 parts books, numbered PR 686 and PR 728, these illustrate everything relative to these two models in minute detail. Copies turn up online occasionally. You want the ones marked "Dernière Edition" if possible.
As regards the earliest surviving R4s, I have seen a few mentions of surviving R3 R1121 (which was an R4 with a 608cc engine) which produced from October 1961 to September 1962 and of which only 2526 were built. There is certainly at least one RHD R4 in this country with a six-figure number plate but this only means it was before 1/1/1965. If yours is R1122 and has a low serial number (nearer 1 than 7216) then it dates from nearer March 1962 and thus must be one of the first six months' production of R4s.
The ISBN-10 for the Séjourné book is 2-85120-482-3. It contains much useful information and illustrations.