sim card slid into the slot without the sim card tray

I would also try a vacuum method. I recommend using the highest power vacuum you have and a balloon. Cut a small slit in the top of the balloon, insert the vacuum hose (with smallest attachment) into the slit for a tight fit. turn on the vacuum and place the end that you would normally blow into around the sim card opening. hope this helps

Heat end of stright pin push into side of sim that.shows.Pull out you might ruin a cheap sim card but phone is not in danger of bad take down and resamble.Hoping as a newby to not break something. I had to use stright pin with a Huawei P 20 .Whivch does not even have a removable back.If that did not work I would have tried to find a way to dismantle it to access the sim.But since I was the stupid idiot who though like a kindle tablet just push it in.Yea way in it went. So maybe safer to have some one else fix if phone very valuable. If cheap go to youtube and watch a video and try.I would have and learned to replace a laptop screen that way.

To get the SIM card out, the easiest (and I use that term lightly) method would be in disassembling the device.

After you remove the back glass and separate the midframe from the LCD frame (with the motherboard), you'll have to get very pointy tipped tweezers and slowly work the SIM card out of the SIM tray mounted on the motherboard. This is the method that may result in the least amount of damage. If any of the pins on the SIM tray get damaged, you'll have to find someone with soldering experience to replace it.

Here is ifixit's guide to removing the motherboard. (I personally prefer high quality playing cards or thin guitar picks for removing the back glass, with the aid of a razor blade to open that initial gap. Just be very careful and maybe order a back glass just to be safe (Back Glass)

Galaxy S6 Edge Motherboard Removal

The SIM tray can easily be found in the ifixit store for a good price.

SIM Tray for Galaxy S6 Edge

First let me say I did not come up with this solution, but Maribel Gonzalez did via Youtube 7 years ago. Reviewing the proposed solutions to the stuck SIM I am compelled to share this because I found it simple and brilliant.

Maribel used an index card and credit card - that combination did not work for me.

Cut a strip of index card and credit card the width of the slim slot - both strips should have some length. (a strip from Equate brand of Nicoderm Packet worked perfectly).

Hold the index strip and cc strip together as one strip - insert into sim slot - push a little xtra into the slot - then very slowly pull the paper out and the sim card should come out far enough for you to get hold of it. I had to do this several times to perfect it - but it works! Good Luck!