To be saved apart from being in the Catholic Church requires “invincible ignorance” (i.e. it isn’t your fault that you aren’t Catholic). The classic case would be an aboriginal tribe somewhere that has never heard the Gospel, or even of Jesus or His Holy Church. Because God doesn’t require the impossible, these people are not damned for not belonging to the Church / believing in the Gospel. However, someone who just doesn’t bother searching wouldn’t be in “invincible ignorance”, wouldn’t be outside the Church through no fault of their own and hence would likely not be saved. Of course, it is impossible to speculate on the state of any individual soul (only God knows what the person’s state is at the moment of death) but overall we can say it isn’t very likely for someone who just doesn’t care to make it to heaven. Remember, Jesus commanded us to “Strive to enter by the narrow gate” (Lk 13:24). Whether or not someone who fills their life with other concerns while neglecting the search for truth is “striving” to make it to Heaven, I’ll leave for you to determine.
At the heart of your question, though, seems to be the mistaken notion that most (or all) people will finally be saved. I suggest you read an excellent book looking at what Vatican 2 teaches about salvation by Dr. Ralph Martin - Will Many Be Saved?