A priest was once asked what Heaven will be like. He told us to close our eyes during a public retreat; they were closed for about three seconds. He then told us to open our eyes. When we sat expectant, waiting for an explanation, he said: “well, here it is”!
When the World ends, time is made redundant, and space becomes infinite, God will live with us in this world - but perfected! Every meadow and glade and street corner from your youth will be there, but greater. All the buildings you explored and forests you got lost in will remain, albeit shining with a glorious light that was not seen before. God wishes to sanctify THIS world, THIS universe, THIS Cosmos with His great love. We don’t know why He created this material existence, other than to perfect it over the great span of time.
Waking up on the last day will be like a winter’s morning for a child, a summer’s morning for a teenager, a spring’s morning for a retired person, and an autumn’s sunrise for the quiet person. All things will be exactly as each person ever dreamed of them being, but here. The only difference will be that God’s own Throne will be established, physically, in a new city somewhere on Earth. We will be with Him, and simultaneously everywhere. Each moment will last as long as we wish, because there will be no moments at all. You may spend 5 000 years sipping wine with your best friend, and at the SAME MOMENT take a leisurely walk of 10 minutes with a crank you never really knew, but who is now healed and greater than we had ever known them.
In short: of course you can give God a hug, once we get our bodies back. Christ our Lord took on real flesh - even this crude matter - and you can bet He hugged Lazarus, his dear friend, if He cried for him.