FYI, if you entertain the possibility that God may be a physical entity, one which encompasses the entire visible universe and beyond, then everything that we see, touch, taste, smell and experience may end up being "objective and verifiable evidence for Him'.
It really depends on how one *defines* God.
I do believe that God sustains the universe as we see it, but this is only temporary in order to fulfill His will.
Isaiah 65:17
"For behold, I create new heavens and a new earth, and the former things shall not be remembered or come into mind"
God acted in more "physical" ways in the Old Testament, but after Jesus sacrifice, everyone who believes in Jesus has access to the Holy Spirit, which is the primary way God now communicates to His followers.
The new heaven and earth will not be "physical" in the way we understand physical, it will be spiritual and we will have new spiritual bodies.
2 Corinthians 5
"For we know that when this earthly tent we live in is taken down (that is, when we die and leave this earthly body), we will have a house in heaven, an eternal body made for us by God himself and not by human hands"
2 Peter 3:13
"But according to his promise we are waiting for new heavens and a new earth in which righteousness dwells"
God will dwell among us in the new Jerusalem.
Revelation 21:2
"And I saw the holy city, new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband."
I would warn to be careful how much stock you put in this physical world we all dwell in now, for evil still resides here, this is why it must be destroyed and made new.
Ephesians 2:2
"In which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience"
If you believe in Jesus, scripture is your best friend because the Holy Spirit confirms it as truth.