You’re trying to index something that belongs to the character, not the player. A rule of thumb is not to parent first before setting properties, because setting properties of an instance that isn’t parented is very cheap and for that reason is good practice.
Instead of explaining the reasons, you can just see it for your self: PSA: Don't use Instance.new() with parent argument
Also there is no need to call FindFirstChild on their character, their character should exist by the time the event is fired and if not, you can use utilize player.CharacterAdded:Wait().
game.ReplicatedStorage.BigBomb.OnServerEvent:Connect(function(player)
local bomb = Instance.new("Explosion")
bomb.BlastRadius = 8
bomb.Position = player.Character.HumanoidRootPart.Position
bomb.Parent = workspace
wait(1)
Bomb:Destroy()
end)