I didn't pack mine until my surprise water break in the middle of the night at 38 weeks. Def. not recommended, but what I *did* do that I would recommend is to make a list of everything you want to put in the bag, and pack it a little at a time. I had a list already written out, so while I was showering before going to the hospital, my husband gathered up everything he could and I just took care of the rest. I don't think you're too early. Good luck with everything!
I did the majority of the packing around 36 weeks. But I also made a list of last minute things to grab and put it on the garage door so we wouldn't forget any of the things we couldn't pack then.
Maybe make a list and make sure you know where everything is now, and then pack it in a week or so? Seems a bit early to pack it now, personally I'd probably end up unpacking and repacking like six times between then and now.
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As PP already mentioned, I would pack what you can now, and then make a list of everything else you will need to throw in there at the last minute and leave it with the bag. This way either you or your DH can grab the bag and the list will readily available for either person to know immediately what else needs thrown in. Starting now will alert you to any items you may still need to purchase and for me it gave me a peace of mind to know it was ready. I packed around 36ish weeks and delivered at 40.
Re: When should I pack the hospital bag?
With you having twins, I would pack soon.
I can't remember exactly, but my bag was ready to go around 36/37 weeks.