What statistical tools can I use to evaluate class comparison over a categorical variable? I'm a noob in statistics so forgive me in advance for misusing some concepts.
I've constructed an analysis counting a categorical variable over 1 million records and got the results below:
Class | Count
---------------
A     | 328362
B     | 328129
C     | 327950
D     | 327220

I'd like to show although class A has the maximum count this may occur by chance and is not that special.
 A: It seems you want to test whether all four categories are equally likely. An appropriate test is a one-sample chi-squared test of the null hypothesis that the four Class probabilities are all $1/4.$
In this case the test statistic is
$$Q = \sum_{j=1}^4 \frac{(X_j - E)^2}{E},$$
where $X_i$ are the frequencies $X_1 =  328,362,$ and so on, and where the expected count in each Class is the average $E =  327,915.2$ of the four frequencies.
Under $H_0,$ the test statistic $Q \stackrel{aprx}{\sim} \mathsf{Chisq}(\text{df}= 5-1=3).$ (For your large counts, the approximation is quite good.)
In R, the procedure chisq.test computes the test
statistic $Q$ and its P-value as follows:
x = c(328362, 328129, 327950, 327220)
chisq.test(x)

        Chi-squared test for given
        probabilities

data:  x
X-squared = 2.2257, df = 3, p-value = 0.5269

Because no probability vector was provided the default
probability $1/4$ are used for each Class.
Because the P-value $0.527 > 0.05$ we have no evidence
at the 5% level to reject $H_0.$ So the data are
consistent with the null hypothesis that all four
groups are equally likely.

The P-value $0.527$ is the area to the right of the solid vertical line at $Q = 2.2257$ under the $\mathsf{Chisq}(3)$ density function. We would have rejected $H_0$ at the 5% level if $Q > 7.815,$ the "critical value" at the vertical
dotted line.
1 -pchisq(2.2257, 3)
[1] 0.526904
qchisq(.95, 3)
[1] 7.814728


