Can I beat Pokémon Scarlet with Hardcore Nuzlocke rules - using ONLY RANDOMIZED pokemon? (No items, No overleveling, Set mode)

HARDCORE NUZLOCKE RULES:
1. Only one Pokemon per area
2. If a Pokemon faints it must be boxed
3. I cannot overlevel beyond the Gym leaders ace
4. No items in battle (held items are okay)
5. No duplicate species can be caught
6. Must nickname Pokemon

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