Even if God did predetermine who would and would not be saved for not other reason than that is what He decided, there is no way for man to be able know if it is true.
Well, our Lord Jesus sure knows who His sheep are. To me it's a blessed thought to know our Lord Jesus sought me, rescued me, and keeps me. And that IS what the Bible says.
You are entirely correct, at the very least in regards to correctly judging the "elect"ness of others. This is where the P in TULIP - the Perseverance of the Saints - comes into play as a visual aid to the observer. None of us - from the Pastor down to the layperson - knows what's in the hearts of that person in the pew next to us, or the church across the street. What we can do is observe their lives, and offer a temporal judgement as to their spiritual condition, tempered as limited to only as much as has been observed. When churches do this, people are either baptized, offered communion, or perhaps branded heretics or excommunicated. Having said a prayer found at the back of a tract may not be enough, at least not from the standpoint of the observer. It wasn't for Saul-turned-Paul. The church in Jerusalem wanted to take a wait-and-see attitude, based upon his past life and recent conversion, but it took a divine act experienced by the observers, to convince them otherwise. Paul's initial testimony did little to convince them.
Barring the witness of a divine act, none of these actions are IMO categorical, final decisions that render a person saved (or damned) eternally. Instead, they are a church's "best guess" as to that person's spiritual state are, and are recognitions (or denials) of temporal grace to that end. There is always a final judgement, and fallen men and women may misjudge (and mis-prosecute) others. But the more grounded in Scripture they are, and the more they are earnestly seeking the Lord's face in their decision-making, the less likely it will be.
Sure man can know it's true.
Why?
Because the Bible tells me so.
May I ask how Revelation says our names are written in the Book of Life before the foundation of the world?
If that doesn't mean our salvation was predetermined by God, what does it mean? And don't say it means he "knew" we would be saved ahead of time and then put our names down. That is just silliness. Why have a book if he wasn't effectively choosing who to save, just looking into some crystal ball? The book is significant. Honestly, it is hard for me to see it being treated with such reverence as a central aspect of salvation if God just decided to write people's names in there when he happened to look into the future and write down the names of those he saw come. No, it is more than that. After all, I do recall Revelation saying we are also his "called, chosen, faithful" followers.
And Romans 9 says some clay is prepared for destruction, some for life. The chapter implies an eternal fixing of this destiny.