Pinning down a solid timeline for Monument Valley is very hard. The levels are completely separate, and there’s few things that carry over between them. But even with this, we can put together something, mostly based on Totem’s appearances and the level subtitles.
Level VI’s subtitle explicitly says that Ida is meeting Totem, implying that this level takes place before any other level including him. He’s shattered in Appendix V of Forgotten Shores and pieced together in Appendix VIII; no levels including him can take place between those two. (The levels including Totem are Levels VI and IX, Appendixes I, V, and VIII, and Ida’s (Red) Dream - surprisingly few, for such a memorable character.) At the end of Appendix VIII, Ida finds herself at the top of a mountain looking up at the Observatory, Level X and the finale of the original game, implying that Appendix VIII is directly followed by Level X.
Level IV’s subtitle is also helpful: In Which Ida Discovers New Ways To Walk. As with Level VI, this is explicitly presented as the first time something has happened. Every level involving walking on oddly-angled surfaces (that is, most of them) takes place after Level IV.
The spirits are largely useless. The information they give is vague at best or referring to a time well before that of the game. The only helpful one, for this purpose, is the one that says that“forgetful princess confuses past, present, and future”. As she is in Forgotten Shores, which was released after the base game but is clearly set during it, this is presumably meant to imply that the timeline did not correlate linearly with release date.
So here’s the information we have. Level IV is set very early on, probably before Ida meets the Totem in level VI. (Ida herself never has to walk on oddly-angled surfaces in Level VI, but she can, and Totem must; it would be odd for her to“discover” this after seeing Totem do it.) Level VI is set before Level IX and Appendixes I, V, and VIII. Level IX and Appendix I must be set before Appendixes V and VIII, but can take place in any order relative to each other. Appendixes V and VIII must be in that order, and Appendix VIII is placed immediately before Level X. Ida’s (Red) Dream can presumably be placed whenever, seeing as it’s a dream. Other than that, there is no solid timeline for the games, and no way to find one. The simplest way to interpret the timeline is to place all of Forgotten Shores immediately after Level IX. This is in keeping with all the information we have, and may be the “intended” timeline. Many more complicated interpretations are possible, though.We just don’t have enough information to determine which makes more sense.