My partner (40M) caught me (32F) in a lie, what can I offer to move forward?

Some background: my partner and I have been together for 2+ years and we share a 1 year old. We met at work and started a relationship from there. Our relationship isn’t the healthiest, some might argue. He has the tendency to stonewall me whenever I bring up a concern or pose a question about his honesty. He has a very black and white view on the world, and is extremely against me having any interactions with the opposite gender outside of work-related topics.

The lie: I know this is going to look bad on my part. I attended a CPR/first-aid class at work yesterday. I have a certification that’s about to expire and the class had low sign-ups so I decided to join. I didn’t mention this to him because we were in the middle of an argument about his IG following (he follows some questionable accounts). During the class there was a joke about doing chest compressions to different songs. After lunch, I saw a Reel about that exact topic and I sent it to the safety manager (M) since everyone had just been talking about it. This morning, my bf asked about my morning at work, and wanting to avoid an argument I lied about how I got signed up for the training and didn’t mention the male safety manager being there. He pretty much grilled me until I finally had to admit that he was there and then he asked to see my phone. I tried to delete the message to the safety manager (I know, I know) but he saw it.

I’m well aware I handled this whole situation in the worst way possible. It was sheer panic. I’m not remotely interested in the safety guy, and I do not find him attractive in any form. But now my partner is saying I was emotionally cheating, and going as far to say that Im probably physically cheating as well. I absolutely am not. He’s still very upset and spent his lunch break grilling me some more, and I’ve acknowledged what I did was wrong.

What can I offer him to move forward? I’ve tried to offer reassurance and transparency, but clearly that’s not enough. Has anyone been in a similar situation?

This isn’t a sympathy post. I’m really just looking for constructive advice on how people have been able to come back from this if possible.

TLDR: I sent a meme to a male coworker that I’m not remotely interested in and lied about it. I tried to delete the message and my partner caught me. How can I reassure him that it was not malicious?