Why did the elders believe that G-d sent Moses (Sh’mot / Exodus 3:16)?
Was it because Moses performed miracles?
Was it because Moses just "showed up?"
The elders of Israel believed Moses because Moses told them a secret message -- one he himself may not have realized was special.
Moses repeated to the elders the very words G-d had spoken through Ya'akov / Jacob and Yoséf / Joseph as a promise long before they were enslaved.
This secret message which Ya'akov / Jacob told his sons and Yoséf / Joseph told his brothers had been passed down to their children and theirs -- a treasure held by the elders of Israel.
Here is what G-d told Moses to say to the elders of Israel:
“'Go, gather the elders of Israel, and say to them, HaShem, the G-d of your fathers, appeared to me - the G-d of Abraham, Isaac and Jacob. He said, 'I have granted you special providence (פָּקֹ֤ד פָּקַ֙דְתִּי֙ / remembered you) regarding what is happening to you in Egypt.” – Sh’mot / Exodus 3:16.
What is so special about that statement from G-d?
Why is it more powerful than a miracle as proof that Moses was sent by G-d?
Yes, G-d gave him a staff that turned into a snake and back again.
Yes, G-d turned his chest diseased and back to health as a sign.
But those were not the reasons the elders believed G-d had sent Moses.
Read Sh’mot / Exodus 3:16 closely and then Read B’reshit / Genesis 50:24:
“Joseph said to his close family, 'I am dying. G-d is sure to grant you special providence (פָּקֹ֧ד יִפְקֹ֣ד / will remember you / will attend to you) and bring you out of this land, to the land that he swore to Abraham, Isaac and Jacob.'”
There is a secret code there – the words of Ya’akov / Jacob are repeated by Moses and this was how the elders knew G-d had sent him.
The secret password (as it were) are the words פָּקֹ֤ד פָּקַ֙דְתִּי֙ / special providence (surely remembered or surely visited)…
Yosef / Joseph tells his brothers (the sons of Ya’akov / Jacob) that G-d will grant special providence / פָּקֹ֧ד יִפְקֹ֣ד.
The verb פָּקֹ֧ד / pakad can have several meanings; according to Bolozky in "501 Hebrew Verbs":
to hold a census
And G-d does not merely use this word once.
He uses it twice.
In a row.
This repetition of the verb implies "surety" – it is said twice!
G-d will "surely remember!"
In other words this is an extremely powerful statement “I will remember! I will remember!!!”
In fact the phrase "פָּקֹד פָּקַדְתִּי" translates as "I have surely remembered!".
When the Torah repeats something, it is because the message is critically important.
In the case of this phrase the repetition of these two verbs appears no less than five times in the T’nach:
"פָּקֹד פָּקַדְתִּי" at Sh’mot / Exodus 3:16;
"פָּקֹד יִפְקֹד" at B’reshit / Genesis 50:24 and 25, Sh’mo t / Exodus 13:19;
"פָּקֹד יִפְקְדֵנִי" at Shmuel Alef / 1 Samuel 20:6.
This coded message is so critical that the Torah repeats it: “Joseph then bound the Israelites by an oath: 'When G-d grants you [this] special providence (פָּקֹ֨ד יִפְקֹ֤ד / will remember you / will attend to you), you must bring my remains out of this place.'” B’reshit / Genesis 50:25.
Moses tells the elders that G-d has granted them special providence / פָּקֹ֤ד פָּקַ֙דְתִּי֙ – just as was prophesied by Jacob not once, but twice.
This is no coincidence – it is G-d letting the Israelites know that Joseph’s words were prophetic – and that prophecy is being fulfilled in the person of Moses.
Go back a bit further to B’reshit / Genesis 21:1: “G-d granted special providence to (remembered / attended to) Sarah as He said He would, and G-d did what He promised for Sarah.”
Rashi in his note on the words וְשָׁמְעוּ לְקֹלֶֽךָ (“and they will listen to your words”) in Sh'mot / Exodus 3:16 wrote: “And they will listen to your voice”—by themselves [i.e. without any further proof of your authenticity]; they will listen to you as soon as you say to them the words: “pakod pakad'ti”, because they have long had a tradition that their chosen redeemer would identify himself by using this specific expression [i.e. the doubled use the verb / pakod / פקד, literally ‘to visit’, “attend,” or ‘remember’]: Ya'akov / Jacob had told them v'élohim pakod yifkod ĕt'chĕm (“and G-d will definitely bear you in mind” [see note below] and Yoséf also told them pakod yifkod ĕlohim ĕt'chĕm “G-d will definitely bear you in mind” (B'réshıt / Genesis 50:25).
Did you notice that in Rashi’s statement both Ya'akov / Jacob and Yoséf / Joseph said “G-d will definitely bear you in mind”?
Yet the Torah has both statements made by Yoséf / Joseph.
Why does Rashi say that the first is by Ya’akov?
Sh'mot / Exodus Rabbah 5:16, a midrash (story) says: “...they had this tradition from Ya'akov / Jacob, because Ya'akov / Jacob had transmitted the secret to Yoséf / Joseph and Yoséf / Joseph had passed it on to his brothers.”
This appears to be the source for Rashi’s statement that both Ya'akov / Jacob and Yoséf / Joseph repeated this important code to the brothers – the sons of Israel (Ya’akov / Jacob)…
Rashi’s claim seems since the prediction about the doubled use of the verb פקד contains an element of prophecy and Yoséf / Joseph was not one of the 48 prophets listed in the Talmud, while his father Ya'akov / Jacob —in common with both of the other Patriarchs—was listed as a prophet.
Whether both Ya'akov / Jacob and Yoséf / Joseph or only Yoséf / Joseph stated the important phrase not once but twice (and Torah, when it repeats, does so because there is something very important to be learned) this very important message was remembered by the generations in slavery – taught from one generation to the next…
These words were said to the children of Ya’akov before they were enslaved.
The important root word used is פָּקֹ֤ד / "pakad."
Although usually translated as “remembered” it actually has a number of meanings including "bear in mind" and "count", not just “remember."
These were special instructions…
Special instructions from a death bed…
Yoséf / Joseph did not tell his brothers יִזְכּוֹר אֱלֹהִים אֶתְכֶם / yizkor elohim et'chem ("G-d will remember you"); what he said was פָּקֹד יִפְקֹד אֱלֹהִים אֶתְכֶם / pakod yifkod elohim et'chem, using the unusual verb פָּקַד pakad – a verb only ever used of G-d – and even more striking the Torah uses a doubled form of the verb, too (פָּקֹד יִפְקֹד / pakod yifkod).
And these are the words used by Moses when he approached the Elders of Israel – and they knew he was sent by G-d. G-d had given them special providence – He had remembered His people in merit of the patriarchs.
Moses was not a member of the Elders – and he did not grow up being taught these secret words.
Moses grew up in Pharaoh’s palace.
During his first outing from the palace he killed the Egyptian taskmaster and went into exile.
How could he have known the phrase that was used?
The Egyptian prince's repetition of the unusual phrase to the elders, who surely remembered Yosef's last words, were proof of prophecy (knowing things that a person could not have known).
And therefore the elders believed him.