On that chart, it starts at $135. That's quite a sum to start with. Why does it only start in 2013 when it started "blowing up" for the first time?
"All time" apparently means "since sometime 2013".
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This is a fascinating question and good catch. The only chart I could find listing anything before 2013 is 99Bitcoins. TradingView history begins in May 2014, and CoinMarketCap goes back to May 5, 2013. The bigger exchanges I checked don't go back that far except for Bitfinex, which starts in January 2013, and for dates during that period Bitfinex only charts weekly changes.
I don't have a definitive answer but will offer two possible explanations. The first is that this lack of price data is related to the March 12, 2013, "accidental hard fork" caused by an undiscovered inconsistency between versions 0.7 and 0.8.0, when a block created by a miner running the newer version was considered invalid by miners running the older one. This would mean that for a short time there wasn't a way to define a price because there wasn't consensus about what wallets held which coins (which led Mt. Gox to temporarily suspend deposits with a subsequent crash in exchange rate).
But the more plausible explanation for why there aren't trading records or a price prior to 2013 is that for there to be "a" publicly available price for any exchangeable asset, there has to be some sort of public market for the asset. BitcoinWiki has a table of prices for periods before 2013, but before March 2010 the price is listed as "basically none." The page also says that on Oct 5, 2009, the first public sale was offered on the New Liberty Standard stock exchange (at a rate of 1 USD/1,309.03 BTC), which is also mentioned in this review of Nathaniel Popper's Digital Gold: Bitcoin and the Inside Story of the Misfits and the Millionaires Trying to Reinvent Money. So before October 2009, there literally wasn't a price (if by "price" we mean the exchange rate denominated in fiat currency). There were no trades (denominated in fiat), hence no trade history.
On March 17, 2010, the first online market exchange, BitcoinMarket.com, began operating. Mt. Gox launched the same year and by 2014 was the largest exchange. Although both companies are now defunct and their trade histories (presumably) not publicly available, 99Bitcoins does list "the" price of bitcoin going back to the day BitcoinMarket.com began operations. For these two companies there likely isn't a publicly available record of trades that would allow for an accurate calculation of an average exchange rate in fiat currency for bitcoin before still-existing exchanges began publishing their trade histories. Exchanges may only publish pricing information from the date they begin operation, and the USD/BTC exchange rates on TradingView are all based on particular exchanges, which is why even their aggregate data may not go back before 2014.