Even after Apple did release the iPhone, the strategy behind Android was entirely focused on competing with Microsoft, not Apple. Google was terrified that Microsoft would get into the smartphone OS market and achieve a dominant position, and then muscle Google out of mobile search and advertising. That's why Android is open source (well, mostly). Google made the Android OS free for manufacturers to use with their phones as a way to get them to use Android instead of a Microsoft OS.
The strategy worked brilliantly. Android has done exactly what Google wanted it to accomplish. Microsoft has never gained any meaningful market share in the smartphone market. And between Android and various deals with Apple, Google has a tremendous presence with smartphone users.
You're thinking of the apocryphal story that Google completely pivoted Android when Eric Schmidt heard about the iPhone at the last Apple board meeting before the iPhone announcement
Buying Android hardly would have triggered anti-trust investigations given Apple's significant market share at the time, and the many other significant competitors (BlackBerry and Nokia just to name two).
Same goes with YouTube - Google bought it before it was a smash success, and before people thought that sort of thing would be a major viewership center.
510 Systems and their self driving car really still isn't a money-making center for Google (nor is self-driving technology for anyone at the moment).
Google Apps is a hard sale against Office 365, etc...
I just don't see how any one of these acquisitions, on their own, would have caused government Anti-Trust inquiries... unless your point is Google operates in too many different markets?