These are great boxes. My kids played with these (looks the same as those pictured) and they are very strong. And my boys were not gentle with them.
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This probably won’t work for BB’s no-plastic restriction. But… it was encouraging to see toys are being made from 100% recycled plastic
More info and styles…
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Markers are plastic.
I think our old Thomas trains and tracks were all wood with magnets that held it together? Doing some quick searching it seems that newer stuff in target has plastic, but maybe the older stuff on eBay or maybe elsewhere is still wood?
I spent so many hours building and rebuilding train tracks layouts covering our basement.
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Dang! 
Wooden blocks? The plain colored ones we had when we were kids with the different sizes and shapes.
Floor puzzles
Wooden bead/stringing set
Art supplies
The older LincolnLog sets had wood slats for roofs.
Music instruments- wood shakers, metal cymbals
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For the 5 year olds, costumes?
Girls have a lot of costumes but boys not so many. One year I made (sewed) costumes for my two kids and their two best friends, a girl and a boy. The girl got a purple (of course) princess with the cone hat with scarfs flowing, a criss cross bodice, and it fit her (she was a little big as a 7? year old and a lot of the disney costumes just didn’t fit). For the boy, I made a knight costume with a silver chest plate, some knee pads, some arm bands, and a cape the looked like a metallic dragon skin. Have to say, it was a big hit.
Now, polyester is technically plastic…(and almost all costumes are made with some kind of polyester)
Domino set?
And as others have mentioned perhaps wood or cardboard blocks, wood or cardboard puzzles, wood cars/trucks.
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A years supply of paper airplanes!! 
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I like that idea. Origami could work too? Some are simple and some could be done with parental help?
https://www.amazon.com/hapray-Origami-Projects-Beginners-Children/dp/B08865WLNB/
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What about a membership to a local children’s museum, a movie theater gift card, or a day at a kids fun zone type gift?
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https://www.fatbraintoys.com/toy_companies/fat_brain_toys/worm_farm.cfm
https://www.fatbraintoys.com/toy_companies/fat_brain_toys/grow_see_vegetable_garden.cfm
Work farm and beg garden……not sure if the clear container you observe the worms or veggies growing in is clear plastic or glass.
My kids loved blocks for years and years. A wooden train set? Jenga? Huge wooden block set—allows many hours of creativity. Membership to children’s museum? Aquarium? Zoo?
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Plan Toys makes loads of wooden toys
Also balance bikes are absolutely wonderful.
Marble runs made out of wooden chutes that you can build in all different configurations are great! If there are younger siblings there can be larger balls that aren’t chokeable (depends on the age). The other great thing with marble runs is you can gift add on pieces later on, too - like spirals, or a back and forth bridge.
Wooden trains and train tracks are VERY fun, and like a marble run you can add more pieces too! Like figure eight tracks, a train turn table, bridges, curves, straight lines.
My son played with all of those things for hours and hours - being able to build all sorts of different configurations was fantastic and if the marbles are deemed to choke able, the wooden trains are large enough that they are fine. Brio trains are great if they’re avoiding branding (like Thomas Trains).
A great place that I used to get all sorts of pieces is: https://woodentracks.com
There is a lot out there! If I were in your shoes I’d do the wooden train tracks and trains - it’s something then can do together and separately for hours and hours. Lots of creative play (and don’t get a “train table” because it constrains what they can build! Having lots of new pieces to add on, and curves and bridges means endless creativity.). Have fun! 
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I gave a 5 year old boy a couple of coin collector booklets and a few fairly old pennies I had found. He loved that for years and was going through his parents (and grandparents) coins for years.
But maybe kids don’t even know what coins are? We, of course, have a Mint in Denver so that’s an added tour I could have taken him to.
Given them an aero garden (which is of course plastic) and have him grow they family’s food.
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Something like this: Amazon.com: SainSmart Jr. Woodworking Building Kit, 4-in-1 Kids STEM Projects Set, DIY Wood Crafts Assembly Toys with Different Combinations for Boys and Girls : Toys & Games
Or maybe gardening stuff with fun seeds?
Costco used to have wooden trains and sets—that’s where we purchased several large sets initially. They were compatible Brio, tho the latter was much more $$$$
Here’s a link for an Amazon set (but I have no personal experience and would recommend reading reviews).
https://www.amazon.com/Track-USA-Accessories-Container-Compatible/dp/B01MXRRMF9
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That’s a nice one…wonder if it’s OK to have a plastic container!
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