Compare means without variance Is it possible to run a hypothesis test on two means in a group when only given the means and no raw data?
For example I have and average over 30 days for both groups- but no data to form a variance on it.

The time series nature of your data means that your observations lack independence. There are ways to deal with time series data, but the usual hypothesis tests like a t-test assume independence. When independence of observations is violated, there is weird behavior. The type I error rate is too high for a true null hypothesis, and the type II error rate is too high for a true null hypothesis. I will give a simulation and graphs showing this.
library(ggplot2)
library(MASS)
set.seed(2021)
N <- 30
B <- 1000
p_ind_ho <- p_dep_ho <- p_ind_ha <- p_dep_ha <- rep(NA, B)
for (i in 1:B){
  
  # Simulate data where mu0 = mu1 = 0 and observations are independent
  #
  x <- rnorm(N)
  y <- rnorm(N)
  
  # Run the t-test, store p-value
  #
  p_ind_ho[i] <- t.test(x, y)$p.value
  
  # Simulate data where mu0 = mu1 and observations are dependent
  #
  x <- c(MASS::mvrnorm(N/2, c(0, 0), matrix(c(1, 0.8, 0.8, 1), 2, 2)))
  y <- c(MASS::mvrnorm(N/2, c(0, 0), matrix(c(1, 0.8, 0.8, 1), 2, 2)))
  
  # Run the t-test, store p-value
  #
  p_dep_ho[i] <- t.test(x, y)$p.value
  
  # Simulate data where mu0 =/= mu1 and observations are independent
  #
  x <- rnorm(N)
  y <- rnorm(N, 0.5)
  
  # Run the t-test, store p-value
  #
  p_ind_ha[i] <- t.test(x, y)$p.value
  
  # Simulate data where mu0 =/= mu1 and observations are dependent
  #
  x <- c(MASS::mvrnorm(N/2, c(0, 0), matrix(c(1, 0.8, 0.8, 1), 2, 2)))
  y <- c(MASS::mvrnorm(N/2, c(0.25, 0.25), matrix(c(1, 0.8, 0.8, 1), 2, 2)))
  
  # Run the t-test, store p-value
  #
  p_dep_ha[i] <- t.test(x, y)$p.value    
  
}

s <- seq(0, 1, 0.001)
d0 <- data.frame(x = s, cdf = ecdf(p_ind_ho)(s), null = "True Null", dependence = "Independent")
d1 <- data.frame(x = s, cdf = ecdf(p_dep_ho)(s), null = "True Null", dependence = "Autocorrelation")
d2 <- data.frame(x = s, cdf = ecdf(p_ind_ha)(s), null = "False Null", dependence = "Independent")
d3 <- data.frame(x = s, cdf = ecdf(p_dep_ha)(s), null = "False Null", dependence = "Autocorrelation")
d <- rbind(d0, d1, d2, d3)
ggplot(d, aes(x = x, y = cdf, col = dependence)) +
  geom_line() +
  geom_point() +
  geom_abline(intercept = 0, slope = 1) +
  facet_grid(~null) +
  theme_bw()


On the left, we see that, when the null is true, the independent data give a uniform distribution of p-values, but the dependent data give a distribution skewed towards rejection, which is undesirable. The test is too powerful.
On the right, we see that, when the null is false, the independent data give a distribution of p-values more skewed towards rejection than the dependent data. The test with independent data is more powerful.
Thus, the dependent data give too many type I errors and too many type II errors, the worst of both worlds!
(Zooming in to $\alpha$ levels of interest with a command like xlim(0, 0.1) does not change the story, and I have played with this with other tests like Wilcoxon, only to get the same result that both error rates are too high.)
