Can I keep my home in divorce if we just purchased it and the deposit was a gift from my father?

Community property is property purchased during marriage.  Each spouse has a one half interest in the community property.
Separate property is property purchased before marriage or after the marriage ends.  A spouse has no claim to the other spouse's separate property.
The gift of the deposit from your father is your separate property regardless of the fact that it occurred during marriage.  Therefore, your spouse would not have any claim to the amount of the deposit.
If additional payments have been made on the house and those payments were from income during marriage, the house is community property and your spouse has a one half interest in the house because income during marriage is community property.
If no additional payments since the deposit have been made on the house, you can argue that since the deposit was a gift which was your separate property, the house should be considered separate property and your spouse has no claim.  That argument will be an uphill battle because your spouse will claim that since the house was purchased during marriage, it is community property to which your spouse has a one half interest.  The outcome of this dispute may be a proportionate interest in the house for both parties.