What are the earliest examples of "simplification"?
On a system level, there was never a movement of simplification until the early 20th century. Chinese characters developed from less refined writing techniques and simpler shapes to more standardised writing styles and characters with more complex structures. This is because simple shapes have two (possibly related) problems:


They're too easy to confuse with other simple shapes;
You can only make so many simple shapes, and there isn't enough of them to represent the basic units of the language.


Chinese characters thus naturally piled on more components to existing characters to make enough distinguishable characters to represent the language sufficiently. Simplifications are therefore relatively rare, and are only one kind of process of how characters have changed in general. Exclusive simplifications (which make a former character obsolete) are close to nonexistent.

This being said, one can sometimes find individual characters that were known to be unambiguously simplified at one stage from a previously more complex character. I'll show two examples, the first which people would be more familiar with but doesn't really fulfil the criterion earliest, the second to actually fulfil this criterion (in an approximate sense).



「与」

「与」is ultimately a corruption of「牙」. As is already known,「与」is a simplified variant of「與」.

春秋金⿱止高君鉦鋮集成423戰國・楚簡106曾侯乙墓竹簡篆舁部說文解字今楷　

西周金⿸尸⿱罒丌敖集成4213戰國・楚簡語叢3.9荊門郭店楚簡篆牙部說文解字東漢隸斥彰長田君斷　今楷　

「與」(Baxter-Sagart OC: /*m-q(r)aʔ/) is comprised of semantic four hands「又又」and phonetic「牙」(/*m-ɢˤ&lt;r&gt;a/).

「牙」was a common phonetic loan for「與」in the Warring States period to the Han Dynasty. Over time,「牙」suffered some shape changes into「与」inside the character「與」(changes outside as a stand-alone character resulted into the modern form of「牙」instead). This leads on to the Shuowen erroneously describing「与」as a component of「與」, and「与」as a separate character from「牙」:

戰國・楚簡語叢3.9荊門郭店楚簡篆勺部說文解字今楷　


《說文》：＂與，黨與也。从舁，从与。，古文與。＂ ✘✘ (「与」is not a separate character from「牙」. Should be 从舁，牙聲)
《說文》：＂与，賜予也。一勺為与。此与與同。＂ ✘✘ (Shuowen shouldn't have this entry at all)


The current form of「与」is a result of an incorrect shape analysis from Shuowen (hence why using Shuowen to demonstrate glyph evolution without checking  modern publications on the subject can lead to serious errors), and is really just「與」, inclusive of its corrupted「牙」component, stripped of its four hands「又又」.


  As mentioned earlier, Chinese characters piled on more components to existing characters to make enough distinguishable characters to represent the language sufficiently. 《荊門郭店楚簡》語叢3.9 is an example where「牙」is used as a phonetic loan or rebus for「與」. What happens when you start using phonetic loan characters? You need another character to represent the original meaning, here demonstrated by piling on more components on to「牙」to distinguish its uses.
  
  戰國・楚簡165曾侯乙墓竹簡隸定「」　
  
  「」is a precursor to「齖」, which has even more components; what looks like「臼」in this character is a shape-approximation of the same picture which forms the bottom part of「齒」.




「⿻人一」(Simplification of「伐」)

Exclusively found in Shang Dynasty oracle bones, the simplified form was dropped relatively quickly.

商甲前7.15.4合集6540商甲佚328合集6363正

「伐」(to behead > kill > attack) is a picture of a person「人」and a dagger-axe「戈」, where earlier forms deliberately drew the blade of「戈」across the neck of「人」, emphasising the meaning to behead.

西周金大保簋集成4140春秋・楚金南疆鉦集成428秦簡日書乙種128睡虎地秦簡今楷　

In the simplified form (佚328 and others), most of the shape of「戈」is removed, with only the blade across the neck remaining. The following is a text sample to demonstrate the usage of this shape.


  《殷虛文字丙編》502
  
  The following text contains both「伐」and its reduced form「⿻人一」, both shown in red. Reading order given by circled numbers ①—⑭.
  
  
  
  
  甲午卜，爭鼎（貞）：羽（翌）乙未用羌？用。（之）日⿱隹（陰）。
  
  (Jiǎwǔ [甲午] day divination [卜]) Oracle Zhēng [爭] asked [貞]:
  
  
  "On the day of yǐwèi [乙未] in the period of yì [翌], sacrifice [use, 用] a  Qiāng person?"
  
  
  (Divined a positive result) "Confirm sacrifice [用]." 
  "That [之] day [日] is cloudy/overcast [陰]".
  
  
  甲午卜，爭鼎：羽乙未勿⿻⿰目目（瞿）用羌？
  
  (Jiǎwǔ day divination) Oracle Zhēng asked:
  
  
  "On the day of yǐwèi in the period of yì, don't [勿] sacrifice a Qiāng person?"
  
  鼎：羽乙未用羌？
  
  Asked:
  
  
  "On the day of yǐwèi in the period of yì, sacrifice a Qiāng person?"
  
  乙未卜，（賓）鼎：以⿱戈止（武）芻？
  
  (Yǐwèi day divination) Oracle Bīn [] asked:
  
  
  "Will the farmers [grass cutters for animal feeding, 芻] be brought over [以] from the land of Wǔ [⿱戈止]?"
  
  以⿱戈止芻？
  
  (Asked again:)
  
  
  "Will the farmers be brought over from the land of Wǔ?"
  
  鼎：弗（其）以⿱戈止芻？
  
  Asked:
  
  
  "Will the farmers not [弗] be brought over from the land of Wǔ?"
  
  㞢（侑）于唐子，「伐」？
  
  (Asked:)
  
  
  "To return favours [侑] to [于] our ancestor Tang [唐子], shall we conduct a beheading [伐] ritual?"
  
  鼎：乎（呼）取⿱子止，「⿻人一」？
  
  Asked:
  
  
  "Beckon [呼] someone to grab [取] a sacrificial person [⿱子止] for a beheading [⿻人一] ritual?"
  
  鼎：（燎）于土（社）？
  
  Asked:
  
  
  "Conduct a bonfire [燎] ritual for the regional gods [社]?"
  
  㞢于父乙？
  
  (Asked:)
  
  
  "Return favours for our ancestor King Fùyǐ [父乙]?"
  
  鼎：（王）㝱（夢），隹（禍）？
  
  Asked:
  
  
  "The king [王] had a dream [夢], will there be disaster [禍]?"
  
  不隹？
  
  (Asked:)
  
  
  "Will there not [不] be disaster?"
  
  鼎：（疒）罒（目）？
  
  Asked:
  
  
  "Will the king suffer an eye [目] disease [疒]?"
  
  鼎：弗罒？
  
  Asked:
  
  
  "Will the king not suffer an eye disease?"
  
  




References:


杜忠誥《說文篆文訛形釋例》
季旭昇《說文新證》
劉翔・陳抗・陳初生・董琨　編　李學勤　審訂《商周古文字讀本》
何琳儀《戰國古文字典：戰國文字聲系》
小學堂
中華語文知識庫


漢字源流

國學大師


郭沫若《甲骨文合集》
中國社會科學院考古研究所《殷周金文集成》
張秉權《殷虛文字丙編》

中國哲學書電子化計劃


宋・徐鉉等奉敕校定　漢・許慎《說文解字》

漢語多功能字庫