You are free to set the deities of your world. See p. 10 of the DMG, under "Gods of Your World":
You can adopt one of these pantheons for your campaign, or pick and
choose deities and ideas from them as you please.
You need to pick their alignment, symbol, and domains. As an example, they might be chaotic neutral, have a roaring dinosaur as their symbol, and have a domain of death or life.
For other titans/gods, make sure you cover most or all of the domains, so your players can pick who to worship and get appropriate benefits.
You also need to decide if they are a pantheon, or individual gods. Whatever you choose is reasonable. Pantheons are more closely knit, and individual gods are more free.
And there's lots of lore from the recent films to help adapt worship to them.
In the event that they fight them, here's a basic stat block made similar to Tiamat's stat block:
Gargantuan monstrosity (titan)
Armor Class 25 (natural armor)
Hit Points 615 (30d20 + 300)
Speed 60 ft., swim 120 ft.
30 Str, 10 Dex, 30 Con, 10 Int, 26 Wis, 8 Cha
Saving Throws Str +19, Dex +9, Wis +17
Skills Nature +17, Perception +26, Religion +17
Damage Immunities acid, cold, fire, lightning, poison; bludgeoning,
piercing, and slashing damage from nonmagical attacks
Condition Immunities blinded, charmed, deafened, frightened,
Senses darkvision 240 ft., truesight 120 ft.
Languages Common, Draconic, Japanese
Challenge 30 (155,000 XP)
Discorporation. When Godzilla drops to 0 hit points or dies, his
body is disabled until a nuclear bomb or a large amount of nuclear
energy is fed to it.
Legendary Resistance (5/Day). If Godzilla fails a saving throw,
he can choose to succeed instead.
Limited Magic Immunity. Unless he wishes to be affected,
Godzilla is immune to spells of 6th level or lower. He has advantage
on saving throws against all other spells and magical effects.
Magic Weapons. Godzilla's weapon attacks are magical.
Resistance. Godzilla is immune to all non magical damage, and
resistant to all magical weapons from those not from the gargantuan monstrosity (titan) type, deities included.
Regeneration. Godzilla regains 30 hit points at the start of
Multiattack. Godzilla can use his Frightful Roar. He then makes
three attacks: two with his claws and one with his tail.
Claw. Melee Weapon Attack: +19 to hit, reach 15 ft., one target.
Hit: 24 (4d6 + 10) slashing damage.
Tail. Melee Weapon Attack: +19 to hit, reach 25 ft., one target.
Hit: 28 (4d8 + 10) piercing damage.
Frightful Roar. Each creature of Godzilla's choice that is
within 240 feet of Godzilla and aware of his presence must succeed on
a DC 26 Wisdom saving throw or become frightened for 1 minute. A
creature can repeat the saving throw at the end of each of its turns,
ending the effect on itself on a success. If a creature's saving throw
is successful or the effect ends for it, the creature is immune to
Godzilla's Frightful Presence for the next 24 hours.
Godzilla can take 3 legendary actions, choosing from the options
below. Only one legendary action option can be used at a time, and
only at the end of another creature's turn. The Godzilla regains spent
legendary actions at the start of its turn.
Nuclear Fire (Costs 2 Actions). Godzilla breathes nuclear fire in
a 120-foot line that is 10 feet wide. Each creature in that line must
make a DC 27 Dexterity saving throw, taking 88 (16d10) lightning
damage on a failed save, or half as much damage on a successful one.
Bite. Melee Weapon Attack: +19 to hit, reach 20 ft., one target.
Hit: 47 (7d10 + 10) bludgeoning damage.