Early surface cover plant for pond

Hi everyone,
We've got a small garden pond (roughly 2m x 1.5) in a full sun position. Our main surface cover plant is frogbit which is only just starting to emerge and spread, and I remember that in previous years it wasn't until mid Summer that it really took off. The pond is very prone to algae building up and I'm guessing the main reason for this is that the surface at the moment is barely covered. I was quite taken with the idea of getting a small lily, like Perrys Baby Red, but I don't think our shelves will allow for enough of a planting depth for it - it'd only have about 10-15cm of water above it, and usually less as the pond evaporates a lot in the Summer. I'm trying to figure out if there is a good surface cover plant that will get going reasonably early in the year, that also doesn't need to be planted very deep - or is a floater like frogbit. Does anyone have any recommendations?
Lucid
We've got a small garden pond (roughly 2m x 1.5) in a full sun position. Our main surface cover plant is frogbit which is only just starting to emerge and spread, and I remember that in previous years it wasn't until mid Summer that it really took off. The pond is very prone to algae building up and I'm guessing the main reason for this is that the surface at the moment is barely covered. I was quite taken with the idea of getting a small lily, like Perrys Baby Red, but I don't think our shelves will allow for enough of a planting depth for it - it'd only have about 10-15cm of water above it, and usually less as the pond evaporates a lot in the Summer. I'm trying to figure out if there is a good surface cover plant that will get going reasonably early in the year, that also doesn't need to be planted very deep - or is a floater like frogbit. Does anyone have any recommendations?
Lucid

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Here is a current photo of the pond (after a huge algae clearout):
I can't quite see to the bottom of the pond at the moment as the water is quite murky, but I am wondering if the oxygenators are still going or if they've died off. If they've died off then I guess that's another potential cause.
Ideally I'd like a plant that will cover at least a 3rd of the surface in Spring, which as you can see above the frogbit isn't anywhere near yet. My partner thinks we could get the water lily as planned, but place the pot on the bottom of the pond. However what I'm not sure on is whether the lily gets going early on, of if it's similar to frogbit and won't have much lily pad coverage for a while?
The good news is the pond is very busy with our smooth newt residents, and we've seen some newt efts already over the last few days. We also both saw a small frog (young adult) but didn't have a camera and no sign of it since. Hopefully we'll have more frogs visiting during the year though.
Lucid
try water hawthorn, it is evergreen and will give you year round coverage.
@josusa47 - thanks for your reply. That's good to know that the lilies aren't quite at the surface yet. We've got the hornwort oxygenator but most of it is underwater still (I'm hoping) and I still can't quite see to the bottom of the pond to check. I have a feeling a lot of places don't sell the Canadian pond weed now because it's an invasive non-native. I'll check it out just in case I'm wrong and as a potential alternative if our hornwort has mostly died off.
@Nanny Beach - Yes, I was hoping to keep potted plants to the shelves to make it easier for access, but whichever I go for out of a lily or water hawthorn will need to be planted on the bottom of the pond as they need that kind of depth. You can get pygmy water lilies but apparently these are really high maintenance.
Lucid