The game is split into two halves. The first is based on The Young Indiana Jones Chronicles, in which you will play as a young Indy exploring various regions with his father. You are required to include a Lillipup nicknamed "Indiana" on your team, similarly to the Partner Pokemon in Let's Go. However, this Lillipup can evolve and eventually become Stoutland, and you will be able to catch many other Pokemon along the way to form whatever kind of team you'd like.
This portion of the game is episodic in nature. Each section takes place in a completely different area in an entirely different region. You will visit all of the mainline regions (except Hisui) and will even get to visit some of the side game regions such as Orre, Oblivia, and Ferrum. There will even be one episode in the Orange Islands. Every episode has different Pokemon you can catch alongside progressing through the short, barely-connected storylines. Some Pokemon can only be caught in certain episodes, so if you miss them, you'll never be able to catch them again. This part of the game does not introduce any new Pokemon, instead strictly sticking to what already exists.
The plot in this section is minimal, simply just establishing Indy's interest in archaeology and showing him grow up alongside his partner Stoutland. The final episode of this half of the game is actually the opening scene from The Last Crusade, featuring Indy stealing an artifact from members of an evil team, but failing to escape and having it taken back. This portion of the game also includes the scene where Indy falls into a train car filled with Ekans and Arbok, cementing his fear of snake Pokemon. It's notable that despite these Pokemon appearing in the game and even being on certain enemy trainer teams, you can never catch them.
The second half of the game is split into the four movies' plots, which are still not connected, but they each contain full storylines. The biggest changes you'll immediately notice is that all references to God, Jesus, and Christianity have been replaced with Arceus.
The first part of the second half is The Temple of Doom, taking place in 1935. Indy is asked by the people of a village in Poke-India (name unconfirmed) to retrieve the Sacred Stone from a palace where the evil Team Thug is found. Team Thug turns out to be a cult worshipping Darkrai, and are sacrificing people and their Pokemon to it. Indy's own Pokemon are captured and brainwashed, forcing him to fight them, but he is able to rescue them. After managing to steal back the Sacred Stone, Indy manages to defeat Team Thug's leaders and return the Stone to its rightful place in a shrine honoring Celebi.
One year later, Indy is tasked with locating the Arc of the Covenant, an ancient artifact linked to Arceus. However, Indy runs afoul of Team Nazi, who is also searching for the Arc. When the Arc is eventually found, the Team Nazi Grunts open it and reveal a regional Ghost/Fairy Spiritomb, which wipes out everyone but Indy and Marion. Indy then gets to battle and catch this Spiritomb if he wants. This Spiritomb is said to be the polar opposite of the Sinnoh Spiritomb, instead being made from a swarm of holy spirits who were sealed away inside the Arc by Arceus himself in order to protect it from evildoers.
In 1938, Indy learns that his father, a researcher studying the Arc Grail, has gone missing. He manages to find his father, but the two of them run into Team Nazi again. They race Team Nazi to find the Grail, eventually locating it at the same time. Indy has to fight an ancient knight trainer and his Noble Kleavor for the Grail, but he loses the Grail soon after, as it cannot be removed from its resting place.
Nineteen years later in 1957, Indy is caught up in a battle against Team Soviet, racing against them to locate a mysterious Crystal. When the Crystal is found, it turns out to be an artifact left behind by Ultra Beasts.