Brilliant Diamond, No Evolution or Breeding

The player can get up to 433 species total (436 with additional save data) in Brilliant Diamond without trading, as described here. Without evolving or breeding any Pokémon, and only collecting evolutionary stages that the player can get in the wild, as a gift, or from an in-game trade, the player can get up to 290 species (293 with extra save data). Of the 433 possible species in Brilliant Diamond, the Pokémon unavailable without evolving or breeding are as follows:

Sinnoh Starter Evolutions (6) - 6 total: The Sinnoh starters are only available in their base forms, leaving their evolutions inaccessible.
Other Starter Evolutions (18) - 24 total: The other regions' starters are only available in their base forms, leaving their evolutions inaccessible.
Stone Evolutions (24) - 48 total: Raichu, Nidoqueen, Nidoking, Clefable, Wigglytuff, Vileplume, Bellossom, Arcanine, Poliwrath, Victreebel, Cloyster, Exeggutor, Starmie, Vaporeon, Jolteon, Flareon, Togekiss, Sunflora, Honchkrow, Shiftry, Gallade, Delcatty, Roserade, and Froslass are inaccessible.
Breeding Pokémon (10) - 58 total: Without the ability to breed, Koffing, Ledyba, Spinarak, Wynaut, Houndour, Taillow, Whismur, Shuppet, Spheal, and Sealeo are inaccessible.
Fossils (5) - 63 total: The Fossils can only be revived into their base forms, leaving their evolutions inaccessible.
Other (80) - 143 total: Metapod, Butterfree, Pidgeotto, Pidgeot, Arbok, Crobat, Parasect, Persian, Rapidash, Magneton, Magnezone, Dodrio, Muk, Hypno, Kingler, Electrode, Marowak, Hitmonlee, Hitmonchan, Hitmontop, Lickilicky, Jynx, Electabuzz, Espeon, Umbreon, Leafeon, Glaceon, Snorlax, Dragonite, Togetic, Xatu, Ampharos, Azumarill, Sudowoodo, Jumpluff, Ambipom, Yanmega, Forretress, Gliscor, Granbull, Weavile, Piloswine, Mamoswine, Mantine, Donphan, Blissey, Tyranitar, Linoone, Cascoon, Dustox, Gardevoir, Masquerain, Breloom, Vigoroth, Slaking, Ninjask, Shedinja, Exploud, Hariyama, Probopass, Aggron, Manectric, Swalot, Grumpig, Flygon, Altaria, Claydol, Milotic, Metang, Metagross, Staraptor, Luxray, Wormadam, Mothim, Vespiquen, Cherrim, Drifblim, Lopunny, Garchomp, and Lucario are inaccessible.

Professor Oak(-ish) Challenge Notes

This just contains a list of areas you can find each Pokémon, ordered as though you are playing a Professor Oak challenge and therefore need to obtain every Pokémon as early as possible.

Pre-Badge 1 (Roark) - 13 Total Pokémon

Badge 1 through Badge 2 (Gardenia) - 54 Total Pokémon

Badge 2 through Badge 3 (Maylene) - 87 Total Pokémon

Badges 3 through 5 (Fantina) - 89 Total Pokémon

Badge 5 through 6 (Byron) - 96 Total Pokémon

Badge 6 through 7 (Candice) - 103 Total Pokémon

Badge 7 through 8 (Volkner) - 116 Total Pokémon

Badge 8 through Elite Four - 249 Total Pokémon

If the player battles every Trainer in the region and makes sure to catch all Pokémon as outlined above, they will actually be able to obtain the National Pokédex before defeating the Elite Four. However, without evolution, the player will need to lose to Cynthia to see her Milotic and Garchomp. Many encounters are tied to obtaining the National Pokédex, and those encounters will all be listed in this section.

Post-Elite Four - National Pokédex - 290 Total Pokémon

If the player has access to Sword/Shield, Let's Go Pikachu/Eevee, or Legends: Arceus save data, the following Pokémon can also be obtained:

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How Many Pokémon Can You Get Without Evolving or Breeding in Pokémon Brilliant Diamond?