There is nothing I am aware of in Scripture that says God cannot be seen today. However, there are verses in Scripture that talk about God not being able to be seen, but those are speaking of God the Father, not the Son. Let’s take a look.

John 1:18 says that no man has seen God at any time. We know this is in reference to God the Father because in John 1:14 it says that the Word, which was God (John 1:1), became flesh and dwelt among us. Whenever John speaks of God after this point in his gospel, it’s in reference to the Father. Furthermore, in John 6:46 Jesus says, “Not that any man has seen the Father, except the One who is from God; He has seen the Father.”  So, God the Father cannot be seen.

We also know from the Old Testament that there are verses that say that God appeared. But, we can see from what Jesus said in John 6:46 above that it was not the Father. Let’s take a look.

1. Gen. 18:1, “Now the LORD appeared to him by the oaks of Mamre, while he was sitting at the tent door in the heat of the day.”
2. Ex. 6:2-3, “God spoke further to Moses and said to him, ‘I am the LORD; and I appeared to Abraham, Isaac, and Jacob, as God Almighty, but by My name LORD I did not make myself known to them.'”
3. Exodus 24:9-11, “Then Moses went up with Aaron, Nadab and Abihu, and seventy of the elders of Israel, and they saw the God of Israel; and under His feet there appeared to be a pavement of sapphire, as clear as the sky itself. Yet He did not stretch out His hand against the nobles of the sons of Israel; and they beheld God, and they ate and drank.”
4. Exodus 33:11, “Thus the LORD used to speak to Moses face to face, just as a man speaks to his friend . . . “
5. Num. 12:6-8, “He [God] said, “Hear now My words: If there is a prophet among you, I, the LORD, shall make Myself known to him in a vision. I shall speak with him in a dream. Not so, with My servant Moses, He is faithful in all My household; with him I speak mouth to mouth, even openly, and not in dark sayings, and he beholds the form of the LORD . . . “

So, the people in the Old Testament were seeing God but not the person of the Father. We are told by Jesus that we cannot see the Father (as is clearly taught by Him in John 6:46). Furthermore . . .

1 Tim. 6:16, “[God, the Father] who alone possesses immortality and dwells in unapproachable light; whom no man has seen or can see.”

God the Father cannot be seen. So when we ask if God can appear today, we would have to say that it would not be God the Father who would appear. Instead, it would have to be the Son, Jesus, who would be seen. So in that sense, yes, God can be seen today, but it would be a manifestation of Jesus.