baseball-reference.com defines first three seasons literally.

See previous post:

Ten year contract for seasons 4-13: 191 batters considered 1903-2018. Sunday, March 10, 2019

That post skips ahead to seasons 4-13. But here are a couple of first three seasons for batters considered in that post:

Willie Mays:

Year	Age	Tm	Lg	G	PA	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	BA	OBP	SLG	OPS	OPS+	TB	GDP	HBP	SH	SF	IBB	Pos	Awards
1951	20	NYG	NL	121	523	464	59	127	22	5	20	68	7	4	57	60	.274	.356	.472	.828	120	219	11	2	1		7	*8	RoY-1
1952	21	NYG	NL	34	144	127	17	30	2	4	4	23	4	1	16	17	.236	.326	.409	.736	102	52	2	1	0		1	8
1953			Did not play in major or minor leagues (Military Service)
1954	23	NYG	NL	151	641	565	119	195	33	13	41	110	8	5	66	57	.345	.411	.667	1.078	175	377	12	2	0	7	14	*8	AS,MVP-1

Now baseball-reference.com did not include 1953 when Mays was in the U.S. Army but it did include his very partial 1952 season, which was cut short by Mays being drafted. Mays was NL MVP in 1954. His ten seasons examined in the previous post were 1955-1964.

Bobby Murcer:

Year	Age	Tm	Lg	G	PA	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	BA	OBP	SLG	OPS	OPS+	TB	GDP	HBP	SH	SF	IBB	Pos	Awards
1965	19	NYY	AL	11	42	37	2	9	0	1	1	4	0	0	5	12	.243	.333	.378	.712	103	14	0	0	0	0	0	6
1966	20	NYY	AL	21	73	69	3	12	1	1	0	5	2	2	4	5	.174	.219	.217	.437	29	15	0	0	0	0	0	6
1969	23	NYY	AL	152	625	564	82	146	24	4	26	82	7	5	50	103	.259	.319	.454	.773	119	256	8	3	2	6	2	*958

Murcer was not explicitly mentioned in the previous post but he was one of the 191 batters considered. Murcer could have been found by clicking the link. Like many, Murcer was a September call up in his first season: debut 9/8/1965. Murcer played 133 minor league games in 1966 and not at all in 1967 and 1968 due Murcer being drafted into the U.S. Army. His ten seasons examined in the previous post were 1970-1979.

I don't know the current rules for determining salary arbitration eligibility but I'm pretty sure that these two historic examples would not have been eligible in 1954 and 1970 respectively.

Despite that the previous post makes valid points.