I’m not sure if it’s possible to remain conscious throughout an entire night’s sleep, but my guess is no - not practically, at least. If it were possible, it would take some intense training and inhuman focus to accomplish.
I’m not sure if you’ve already looked at them, but the WILD FAQ and WILD tutorial posted here have some good advice on what to look for when entering a dream and what to do if you’re stuck at a certain phase of WILD:
https://community.ld4all.com/t/the-wild-faq/31294
https://community.ld4all.com/t/wild-an-user-friendly-tutorial/31684
In short, what Spider said in the FAQ is to wait for a full-fledged hypnagogic hallucination (HH) - as opposed to just a hypnagogic image (HI) - before attempting to “step into” a dream.
In the tutorial, Mew151 has some example images that demonstrate the difference between partial HH and complete dream scenes, the latter being what you should be looking to enter.