Work with your DM
As a player, there isn't much available to you that is under your control in this concept, but there are things that a DM can modify, so pitch your idea and see what they say. One thing to clarify would be in terms of leveling. If you are truly a cat who can assume the form of a human, how are both of these forms affected by leveling? Which gets more powerful, and how - or do they both? Does your cat form have class abilities? Once these details are worked out, you might consider one of the following:
Suggestion: modified Changeling race
The Changeling is a race available to PCs and can be found in Mordenkainen Presents: Monsters of the Multiverse and Eberron - Rising from the Last War. Their central ability is described as:
Shapechanger. As an action, you can change your appearance and your voice. You determine the specifics of the changes, including your coloration, hair length, and sex. You can also adjust your height and weight and can change your size between Medium and Small. You can make yourself appear as a member of another race, though none of your game statistics change. You can’t duplicate the appearance of an individual you’ve never seen, and you must adopt a form that has the same basic arrangement of limbs that you have. Your clothing and equipment aren’t changed by this trait.
You stay in the new form until you use an action to revert to your true form or until you die.
In general, what you are asking for is considerably less powerful then this, since you would have only two end forms, human and cat, and since the cat form would presumably be Tiny rather than Small. Because of this downgrade, as a DM, I would overlook the 'basic arrangement of limbs' clause and be reasonably generous in working out the other benefits of the race.
Suggestion: Weretiger, without the resistances
PCs are permitted to be lycanthropes. The weretiger, capable of changing into a powerful tiger, and with immunity to non-magical, non-silvered attacks, is far too powerful for a first level PC. But if we discard the resistances and the hybrid form, make the human form conform to a human of equivalent level as your PC, and have its shapingchanging ability access your true cat form, with an appropriate stat block for a cat rather than a tiger, that seems about right. As written, weretiger PCs have a minimum Str of 17 - we could make this ability score one that ties better into your concept of the magical cat race.