Of course we have. It was in episode 23'. It's also been shown more clearly in some supplemental material, but the point is that was in the actual show. You don't need any lower-tier material to see it. Whether you consider the CI canon or not, that image irrefutably shows how Unit 01 was created from Lilith: they were connected at the legs.
When we next see Lilith chronologically, and in fact when we see her for the first time as far as the series goes...
Her legs are gone and the Spear of Longinus is sticking into her chest. Lilith remains that way until episode 22', when Rei removes the Spear and Lilith regenerates her legs:
From that, we can tell (and this isn't just a conjectural hypothesis, but an obvious fact) that the Spear was stopping Lilith from regenerating. Thus, until the Spear was removed, Lilith could not regrow the legs that she lost.
Wait, what? The legs that she lost? When did Lilith lose her legs? Adam was blown to pieces during Second Impact, but not Lilith. In fact, in episode 23', we can see what Lilith looked like when she was first discovered by the Katsuragi Expedition:
You can't see it that clearly in this image, but in the Test Type OP, you can more easily tell that Lilith's legs are still present:
You still can't see her whole legs, but the parts you can't see are probably buried underground (as her arms almost certainly are.) Even if you choose not to believe for some reason that, since you can't see most of Lilith's legs, she doesn't have any, Lilith still has clearly visible thighs, and what appears to be a knee, which is certainly more than she has when she's crucified and has the Spear sticking into her. [EDIT: I have just been informed that this picture is actually of Adam. However, Lilith still has no reason for her legs to be missing until Unit 01's creation. Even if they were destroyed at some point, they should have regenerated without the SoL sticking into her. And, if this picture is indeed of Adam, that means that, at this point, Lilith could not have the Spear stuck into her, as there is only one remaining spear, and it would be stuck in Adam at this point.]
So, where did her legs go? That should be incredibly obvious. Since I already have the Test Type OP open, I'll go ahead and post a cap of what Unit 01's birth looks like without all those pesky Reis in the background:
It should also be quite obvious from this that the reason Lilith's legs were missing is because they were used to create Unit 01. I can't believe it took me that long to realize this, since everything you need to do so is right within the show itself. And, apparently, this isn't a new discovery at all, but one that, at the latest, MDWigs discovered back in April of 2002 on a different board. I suppose it's too obvious to have gone unnoticed until now, but still... I was hoping I had uncovered something. However, the important thing is:
Lilith's legs are gone because they were used as the material to create Unit 01. It's all right there in the show; you can't argue with it.
Now, onto the case of Shinji Ikari. In the first episode, Shinji stated that he had never seen an Evangelion before (specifically Evangelion Unit 01). Despite this, we know from episodes 21 and 23 that Shinji had seen Unit 01 when he was much younger. In episode 23, Ritsuko says the following:
Ritsuko wrote:This is also the place where your mother disappeared. You probably don't remember, but you were watching it, watching the moment when she disappeared.
Indeed li'l Shin-chan was there at the moment his mother disappeared. We see this in episode 21:
Why didn't he remember seeing Unit 01? After all, an Evangelion isn't exactly something ordinary enough to be easily forgotten. The most obvious explanation is that Shinji was very young and his mother's disappearance must have been rather traumatic. Still, shouldn't seeing Unit 01 again at NERV in the first episode jogged his memory?
No. It wouldn't have, as when Shinji first saw Unit 01, she looked completely different. Olivier Hagué transcribed the following from the liner notes of Genesis 0:12:
Eva Tomo no Kai wrote:"Sono naki ni yokotawatta nitai no kyojin no eizô ga aru. Kore wa Yui ga shôshitsu shiteshimatta jikken o shita dankai de, Lilith to Eva Shogôki dearu rashii. Tomo ni kahanshin ga hotondo nai jôtai deari, ketsuraku shita kahanshin dôshi ga tsunagatteiru yô da. Lilith to Shogôki ga tsunagatta jôtai de Yui wa, Lilith ni sesshoku shi torikomareteshimatta no darô."
According to MDWigs, what this text explains is that, when Yui disappeared, Lilith and Unit 01 were still attached. And, from the Reiquarium image, we know what Unit 01 looked like when attached to Lilith. She wasn't wearing any armor, and her face was covered by a tarp. Since this is what she looked like when Yui disappeared, this is, without any doubt, what Shinji saw in the screenshot I posted from episode 21. In other words, even if Shinji had remembered seeing Unit 01 before, when they reunited in 2015, she would have been completely unrecognizable. To summarize:
Shinji's encounter with Unit 01 when he was younger was at the point when Unit 01 was still attached to Lilith. The Unit 01 that he saw in 2015 was completely unrecognizable based on his previous encounter.
None of this is fanwanking. It is all self-evident. However, since when I stated this information on the IRC, several people seemed to disagree with or misunderstand what I was saying, I felt I needed to post it here in greater detail.