What is the most efficient way to obtain Acquaint Fate?

There are several sources for Acquaint Fates. The most obvious is to simply purchase them with Primogems. However, this is usually not advisable, since all the characters found in Wanderlust Invocation can also be found in the event banners.

The "renewable" options are:

• Receive them from the Battle Pass.
• Buy them from Paimon's Bargains for 5 Masterless Starglitter (unlimited), or 75 Masterless Stardust (5x / month).
  You should be aiming to purchase all 5 Intertwined Fates and all 5 Acquaint Fates using Stardust every month, if possible. Starglitter should be saved for either Intertwined Fates, characters, or shop-exclusive weapons in the Blackcliff or Royal weapon sets.

The progression-based options are:

• Ascend characters. Reaching Ascension Level 1, 3, or 5 will reward you with 1 Acquaint Fate per character. Generally, the first ascension for every character is very inexpensive, so you should be ascending each character at least once, even if you don't plan to play them.
• Unlock new World Levels through Adventure Rank Ascension Quests.
• Level up the Frostbearing Tree in Dragonspine. The ranks that reward Fates are not time-gated, but further levels have a weekly quest component.
• Level up the Sacred Sakura in Inazuma.

If your goal is to grind out Acquaint Fates, note only the Frostbearing Tree and the Sakred Sakura are not time-gated in any way.