I can talk about this with some authority, because I did this myself in my first year cycling. Four or five times a week, out cycling as far as possible, and always with my eye on the average speed. Several times I would get home so exhausted that I would have to it down for a while, my legs unable to support me.
Every week I had to go further and faster. After about four or five months I had simply done too much. I was becoming ill, catching colds, spraining my wrists, and lost the desire to cycle.
I thought it was because of the illnesses and injuries, but in fact I now realise these were in turn caused by the cycling. So yes, you can probably achieve more than I suggest above in the first few weeks and months, but there is a realistic possibility that you will turn off cycling altogether.
Sometimes go out cycling with the sole goal of enjoying yourself. Take it easy, go slowly up the hills, stop for a drink or to take a picture. I do this when I am keen to get out cycling but know I've done too much already in the preceding days.
Never lose sight of the fact that your cycling is supposed to be fun, and try and have rest days between cycling days. These rest days are as important for your physical development as the cycling itself. If you really don't feel like cycling one day, don't.
If you are cycling hard every day, your leg muscles will never be recovering, and it is this recovery process that builds the muscles. Quite simply, it is counter productive to do too much.
Try and see your cycling as a lifelong adventure, not a one-month challenge to be the next Lance Armstrong.
There are lots of cyclists in their 60s who put many a younger cyclist to shame, simply because over the years and decades they have built up the underlying strength, stamina and physique to continue. much more effective than a three month spell of overtraining followed by a bike gathering dust in your garage.