I lost my sim card to this new cell phone I bought from Boost Mobile it's an LG Stylo LG IS 770 and I have not activated yet. Will I be able to activate without Sim Card?

Ricco, Boost Mobile links below, you may be able to activate with out sim card, or no need to wait if you have a retailer near by. Contact them through links below.Check the attached links,instruction and guides, Good luck
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No, you'll have to have a new sim card sent to you. Just call boost, and let them know that you lost it, and they'll send you a new one... shouldn't take but 2 or 3 days. They might not even charge for it.

I have met the same problem, it is really bad experience. so my friend recommend me install LEO Privacy. If a person pick up your phone it take a picture I'm that person is holding your phone so if you lose your phone it takes a picture of your phone and you try to find your phone over the other and then you got a picture of the thief or the person that took your phone from your personal possession or home I like it
LEO Privacy Applock Boost Hide Android Apps on Google Play