gg5, prog, wisdom
うかがい知れない	4,990

うかがい知れない is also quite common. I don't think a note is needed here. It would be difficult to make it concise.
Dropping 窺いしる.

@@ -13,4 +12,0 @@
-<k_ele>
-<keb>窺いしる</keb>
-<ke_inf>&sK;</ke_inf>
-</k_ele>
@@ -23,2 +18,0 @@
-<xref type="see" seq="1172230">窺う・うかがう・3</xref>
-<s_inf>esp. ~ことができる・できない</s_inf>
@@ -26 +19,0 @@
-<gloss>to guess (correctly, based on available evidence)</gloss>
@@ -28 +21,8 @@
-<gloss>to perceive</gloss>
+<gloss>to get an idea of</gloss>
+<gloss>to tell</gloss>
+<gloss>to imagine</gloss>
+<gloss>to guess</gloss>
+<gloss>to grasp</gloss>
+<gloss>to fathom</gloss>
+<gloss>to understand</gloss>
+<gloss>to know</gloss>

うかがい知る	29022	43.2%
窺い知る	22294	33.2%
伺い知る	15834	23.6%
窺いしる	40	0.1%

https://proverb-encyclopedia.com/dictionary/ukagaisiru/
表面に現れていない事柄についておおよその見当をつける。察知する。



うかがい知る	29022	  
うかがい知ること	23967	   <-- look at how common this is (beginning of ことが出来る　ことが出来る
うかがい知ることが	17999	  
うかがい知ることができ	7874	 

https://hinative.com/questions/215004
What does うかがい知る mean?
nobu_japan
figure out


joealvo
10 Nov 2015
 Japanese
うかがい知る＝to guess about something that's hidden behind/that lays behind what you can see/what you know
広辞苑(Koujien) says:
表面に現れていない事柄について、おおよその検討をつけること

彼は無表情だったので、彼の感情をうかがい知ることはできなかった。
I couldn't see what he was feeling inside because he was showing no expressions on his face.

reverso:
You can figure out the class of vegetarians from the twofold increase in the number of vegetarians over the past 10 years...
菜食主義者の層を窺い知ることが出来ます。 (also dekiru)


https://dict.line.me/enjadict/search?range=example&query=guess what
You can guess what the current situation of emergency medical service is like through [from] the results of this survey. → うかがいしる[窺い知る]
この調査結果から救急医療の実態をうかがい知ることができる

Definitions are all about knowing an under-the-surface fact based on the information one is able to see (inference). 

"to infer" is already baked into 窺う。 Reverso often glosses things like うかがい知ることができる as "able to guess" with the implication that the "guess" is correct. 知る may also be adding that nuance.

sankoku's example also uses the うかがい知ることができる structure (他人にはうかがい知ることができない). 
defn: 外に現れたことから、中の様子を知る。

proverb-encyclopedia gives a synonym of 察知, which we gloss as:
to sense; to infer; to gather; to pick up on; to get wind of; to perceive

These seem consistent with the many examples in reverso.

As a gloss, "understand" in particular seems to discard all sense of nuance. (I am sure there are situations it could be used, but it doesn't seem like a particularly good general choice).

The great majority of reverso examples (and there are a good number) are of the ことが出来る・できない　structure
https://context.reverso.net/translation/japanese-english/うかがい知る

The volunteered hinative example also used this structure, as did the random examples I found when looking for evidence of "figure out".

"to see" , as in "are able to see, are unable to see..." is actually one of the most common reverso glosses.  I'm sure my "to guess" parenthetical remark already doesn't look great. I'm not sure what I'd want to add "too see" to this list.　　Similar for "to tell", "they couldn't tell what he was thinking (because his displayed no outward signs")

@@ -14,0 +15 @@
+<ke_inf>&sK;</ke_inf>
@@ -21,0 +23,5 @@
+<xref type="see" seq="1172230">窺う・うかがう・3</xref>
+<s_inf>esp. ~ことができる・できない</s_inf>
+<gloss>to infer</gloss>
+<gloss>to guess (correctly, based on available evidence)</gloss>
+<gloss>to figure out</gloss>
@@ -23 +28,0 @@
-<gloss>to understand</gloss>

Ngrams, GG5 (窺い知る as headword, うかがい知る in examples.)

@@ -4,0 +4,3 @@
+<k_ele>
+<keb>うかがい知る</keb>
+</k_ele>

伺い知る gets more hits

@@ -8,1 +8,1 @@
-<keb>窺いしる</keb>
+<keb>伺い知る</keb>
@@ -11,1 +11,1 @@
-<keb>伺い知る</keb>
+<keb>窺いしる</keb>