How To Mitigate The Random Factor In Agricola?
It sounds like it's not the randomness of the action spaces that bothers you, but the unknown factor. If you're playing in person and others share your opinion, I'd suggest revealing the cards after they're shuffled and just use something else to track what round you're on. You'd have to keep an eye on upkeep to make sure you're not letting things accumulate too early, but that seems like it would address all the concerns you brought up.

If you want to play with the rules as written, you really can't assume that something will come up in any particular spot. For the first Family Growth, what you're describing is exactly the dilemma; if you invest early actions in the hopes of growing your family in Round 5, you have no way of knowing if that will pay off or not, and that's not something that will change with experience. You just need to factor your decision to build early (or not) with the possibility that it will not work out for you. I don't think there's anything you can do about that. For the second family growth, if it's that important to your strategy to get that first, I would say plan on being the start player in both Round 12 and Round 13, probably holding back some Minor Improvements so that it's not a total "waste" of the first move in Round 12 if the Family Growth action isn't the one that comes up.

In general, I think your question is looking at Family Growth in a vacuum, which seems to run contrary to the idea of Agricola. The best path to victory (generally) is diversity, and I realize that Family Growth is instrumental to that since it gives you precious additional actions, but regardless of what you're trying to do, relying on a specific space to be there exactly when you need it is risky. Competent opponents will often block you if possible (since there are few actions that would be detrimental, only slightly less attractive in a vacuum that would be pushed over if it both benefits them and hurts you), and if you spend too much time trying to manipulate turn order, you won't do well. Agricola is also not Chess; the random bits mean that there's not really an "if X, do Y" truism that will be a silver bullet winning strategy.

The way the question is worded makes it sound almost like you consider Agricola to be a zero-sum game, but it's not - it's more along the lines of a Nash equilibrium, even when played two player. I guess my answer to your question would be to "always have a plan B", or maybe plans 1-n where n=the number of players. If you have multiple viable options at all times, you can't be blocked easily (I've never seen the entire table collectively decide to leader-bash in Agricola, and I play with a cutthroat group of people). Ways to do this will vary considerably with the cards you get, the cards your opponents get, and what their biases are (e.g., I've played games where the 3 Wood space was taken literally every Round because most of the table thought they needed to have a 5 room house and use all of their wooden bits - as you may imagine, that took a big strategy adjustment). If you're looking to master Agricola, I think the best thing to do would be to understand how ROI works with scoring in the different categories and watch what everyone else is likely to go for. This extremely long analysis might be a good place to start in terms of Agricola's in-game economy.