The problem was that the gun-type design for uranium required a relatively large amount of fissile material to work. So Little Boy used 64 kg of high-enriched uranium (HEU). By the summer of 1945 they were producing something like 7-8 kg of HEU per month, and by the time of the Trinity test they had about 74 kg of HEU on hand total.

So if they had tested Little Boy at Trinity, they would have only had ~10 kg of uranium left, and it would have taken them another seven months or so to get enough to make another bomb.

Similarly, if they had only developed the Little Boy bomb, it would have essentially been a one-off weapon, with another one half a year away.

Implosion by contrast only required 6.2 kg of plutonium-239 to work. The three Hanford reactors were each designed to produce about 6.7 kg of plutonium per month at maximum power. So in theory the site could produce over three weapons a month using plutonium implosion. (In practice their production rate didn't get that high, but it was still much higher than the U-235 route.)

So implosion promised them multiple weapons, both for the war and the postwar. And if you could get implosion to work, you could also adapt it for hybrid ("composite") uranium/plutonium implosion bombs, which would be a much better use of uranium than the gun-type bomb (it would require only a few kilograms worth of uranium, and they would be slightly more powerful than regular implosion bombs).

So you can see from a technical view why implosion became important — it would really stretch out their fissile material supplies and it would allow them to use plutonium, which was otherwise useless if they couldn't figure it out.

As for why they tested the plutonium gadget and not a uranium one — for one thing, again, they only had enough fuel for one Little Boy bomb. So testing was not an option. But more to the point, they didn't feel that they needed to test it. The Little Boy bomb's action can be approximated and estimated through experiments that form critical masses for just a moment (the so-called "Tickling the Dragon's Tail" experiments). It was from a scientific point of view a very conservative device. They were not very worried about its performance.

The implosion bomb was a much trickier thing and its success could not really be estimated without a full-scale detonation. And indeed, the test at Trinity exceeded their most optimistic calculations by a factor of four. So it was a very chancy sort of thing, where the Little Boy was, by and large, seen as pretty clear cut.

The really interesting historical question is why they dropped Little Boy at all. Why not take it apart and use it to stretch the implosion bomb supply? They figured that Little Boy had enough fissile material in it to make half a dozen more implosion weapons, if they had used it to augment the plutonium supply. Oppenheimer explicitly proposed this to Groves after Trinity. Groves said there wouldn't be enough time (Oppenheimer thought it might take a month to make the changes). Which is an interesting thing to contemplate — in order to have two bombs to drop on Japan by early August (a third plutonium bomb was scheduled for mid August), Groves was willing to undercut the stockpile by a significant factor.