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When Jim Gordon learned he was going to be partnered with an Alpha he knew he was going to be going through way more shit than necessary, especially after taking note of Bullock's charming personality.
In the end he got used to it, though he was uncomfortable every time Bullock abused his Alpha status to get someone to talk. Betas like him could manage themselves but the moment Bullock found out an Omega was a suspect he volunteered to handle him, and it made Gordon sick. It's one of the first laws of ethics you get taught, and apparently one of the ones the Gotham PD had completely forgotten about.
It was one of those days when Jim noticed Ed across the room glaring daggers at Bullock as he escorted what wasn't even a suspect, but a witness, into the interrogation room. Jim felt a feeling of camaraderie with Ed grow right there, the one other person in the room who thought this was morally objectionable. After that he tended to gravitate towards the forensic scientist when he had nothing better to do.
He found out that Ed was actually quite funny when he had the chance to feel comfortable, and that he was fond of video games, though he didn't get to play much any more, something they both had in common. They started taking lunch together more often than not, which is how he learned that Edward was a fairly good cook, bringing fully balanced meals packed in Tupperware containers. They would spend that time cracking jokes about their co-workers and later, when they felt more secure in each other's company, how they would re-structure things if they were in charge. Ed became his best friend and ally, and it all started because, well.
You can't spend that much time with a person and not see through the suppressors, especially when your lunch buddy always takes a pill when your head is turned. Ed was an Omega with a serious fear of losing his senses and Jim understood it was best that he never acknowledge it out loud. Jim understood that desire to not get lost in someone else, unsure where affection ended and dynamics began.
That's why he always went after other betas, like Barbara, though they couldn't stay together in the end, they never had to have that worry. Barbara couldn't get involved in all this, but Ed already was. That was a thought that kept surging through Jim's head when he was in his friend's company. He wanted to see how far the other's affection ran, but he was afraid because every day they were together, he could feel dynamics take hold.