It could be possible by teleporting you and the iron golem with relative positions and so on, but it would be so glitchy that a mod or even a plugin would make it a way easier task to accomplish and have result in a successful attempt without having thousands of command blocks with different tick delays to ensure it runs constantly at the game's framerate.
In a simplier way to phrase it:
Make a mod or plugin for that. It will get you the wanted result with way less hassle achieving it.
As the other people have said, the best way is to write a mod. However, you can summon a boat or minecart that is riding a iron golem, and you would be able to ride the boat/minecart and sorta ride the golem underneath. You won't be able to control the golem though, and having a minecart or boat looks ugly.
One way I could see it work that way (using the method you wrote above.) is by using the same method as the pigs uses or a similar method. You could place an armor stand in front of it following your player's forward vector and then make the iron golem move towards it (Not even sure it would work the way I think, but it would be close enough to a real-like movement.)
But the problem then comes to applying this to multiple users. Which could require a lot more command blocks which would render this contraption eating at least ten to fifteen times the required resources a plugin or mod needs.
The best way I could suggest to use would be with a plugin so the player does not have to download any extra resources to play the server only for a feature the player might not even use that often. (I cannot remember when was the last time I used a pig or horse for travelling.)