I think that both「ついてこそ」and「ついたからこそ」can be fit into the above sentence. However, the textbook gives「ついてこそ」as the right answer and I don't know why.
Using ～た sounds like it's confined to one specific instance and not a general statement. If the rest of the sentence was also ～た it would be ok IMO, but again different from what the general statement is saying.
Think also about what ～て implies with respect to aspect: completeness of the action.
It is precisely by having got into the most routine of routines -- get up in the morning -- that one can move on to other activities.
「朝、起きる」という生活習慣が身についてこそ、次の行為へとつながっていくのだ。 Only when you acquire/learn the habit of getting up early, the next step will follow.
「朝、起きる」という生活習慣が身についたからこそ、次の行為へとつながったのだ。(or つながっていったのだ。）。Only because he acquired/learned the habit of getting up early, his next step followed.