I hope this helps, turned out longer than I intended lol
What I've seen so far in most non-linear stories, is that the non-linear aspect is explained pretty early.
"I'm a Spider, So What?" has issues because of this, the first flashforward was pretty late into the story, and the audience got confused. The author had to explain themselves and all. It was a pretty messy thing if I'm recalling correctly.
Others have the second chapter introducing the non-linearity. Usually with newspapers, Television, the radio, etc. letting the audience know the date, hour, year, etc. through dialogues coming from them.
Like a lot of Cyberpunk, Steampunk, and Sci-fi fiction, having the world explain itself is a very good tool.
In cyberpunk 2077, we can see the advertisements all around the city relaying information about the world instead of having an NPC breathing down our necks saying that Militech has the best bio-software or whatever the name was. Similarly, the character in your story can stop and read the newspaper, or check twitter, or a novel release and mention the date.
For example, over ten years ago, I wrote a series of short stories about a group of immortals living their lives in a massive city housing the entirity of humanity in the far future(never published it, i cringe when i read it). I used the radio, smartphones, and holograms to relay passage of time and what year that specific part of the story took place in, since people don't usually say "Hello, nautics, what a beautiful day is this 18 of June of the Year 2021. Don't you agree?" "Oh yes, AliceShiki, I love that it's 0:22 right now and the weather is freezing cold in South America."
It could be for example two people conversing and the radio in the background states an election, event, or a STORM THAT IS APPROAAACHING, which you stated in previous chapters had already passed through character dialogue or the state of the world around the characters(banners, uprooted trees, covered windows, no cars on the streets). The readers will then understand that that point of the story is before the previous chapter.
While convoluted, it's not hard to do, and not harder to understand. You could use the state of the characters belongings, and even their own bodies if they have suffered injury to relay time. A scar, a missing finger, piercings, bracers, beard, length of hair, sun tan, a broken glass, a shatered mug that was glued back together, ripped clothes, etc.
So what I mean is, go ahead and have fun. Be sure to give attention to the details that will let the audience know which part of the story they are reading, and don't be discourage if you don't know how to do it.