The exodus from Egypt was in Nissan 2448. The children of Israel entered the land of Israel after 40 years in the desert in Nissan of 2488. It took 14 years to capture and inherit the land until Nissan 2502. Why wasn’t 2502 the first year of shemita? Rather, shemita starts with a full year, so shemita started in Tishrei 2503.
Erachin 12b states that the first Beit Hamikdash was destroyed in the first year of shemita. It further states that the children of Israel were in the land for 850 years (17 jubilees of 50 years) and not counting the first fourteen years for shemita (leaving 836 years), according to the Rabbis, after 800 years, the 36th year of the jubilee is the first year of shemita. Accordingly, 2503 was the first year of shemita, 3502 was a jubilee, and 3338 was the 36th year of the jubilee, the first year of shemita. Seder Olam Zuta (chapter 1) also dates the first expulsion from the land of Israel in 3338. This is the year that the first Beit Hamikdash was destroyed.
Erachin 12b further states that had they counted the first fourteen years, the destruction in the 850th year would be in the jubilee (see Rashi). The first of the 850 years is 2489 with 3338 as the 17th jubilee. Although they entered the land in Nissan 2488, the 17 jubilees start with a full year in Tishrei 2489.
Rashi A”Z 9a states that the first Beit Hamikdash stood for 410 years and gives the year 3338. Rashi holds it was built in 2828. Rashi may count 410 years excluding the year of its destruction in the 411th year, or he may exclude the year it started. Seder Olam makes no mention of 410 years.
Erachin 12b further states that the second Beit Hamikdash stood for 420 years and (like the first Beit Hamikdash) was also destroyed in the first year of shemita. A new wave of shemita started with the second Beit Hamikdash. R’ Yehuda uses all 420 years for 60 cycles of 7 years. The next year was the first year of shemita. The Rishonim explain that the second Beit Hamikdash was destroyed in the 421st year. Rav Ashi (13a) explains the Rabbis by removing six years. 414 years (instead of 420) is shemita and the 421st year was the first year of shemita. Rav Ashi explains that shemita did not start in the second Beit Hamikdash until Ezra came up and sanctified it. Rashi explains that the second Beit Hamikdash started in the second year of Daryavesh, Ezra came up in Av of the 7th year of Daryavesh in the 6th year of the Beit Hamikdash, and he started counting shemita from Tishrei of the 7th year. We again see shemita starting with a full year.
Rashi A”Z 9a holds that the second Beit Hamikdash was not destroyed after the 420 years, but in the 420th year in year 3828 (starting from 3409) with 172 years remaining (after the year of the destruction) until year 4000. Tosafot (Rashbam and R”T) there argue on Rashi, based on Erachin 12b-13a, and hold that it was destroyed in the 421st year (3829) with 171 years remaining until year 4000. The Tur (Choshen Mishpat 67) says that this is also the opinion of the R”I. The issue against Rashi is that the 420th year (3828) is shemita. Rashi (A”Z 9b) explains that Rav Ashi’s 7th year restart is (also) according to R’ Yehuda. Rashi decides like R’ Yehuda (based on A”Z 9b), with the 420th year starting from the 7th year being the first year of shemita.
The Rishonim and halachic authorities explain that shemita is one year earlier according to Rashi (A”Z). The Rambam for shemita purposes agrees with Rashbam, R”T, and R”I that 3829 was the first year of shemita. The Rambam further explains that the geonim rule like the Rabbis (against R’ Yehuda), but they agree with 7 year cycles after the destruction. In any case, the 420 years of the second Beit Hamikdash are from 3409 to 3828.