Error: please supply starting values

I am conducting a log binomial regression in R. I want to control for covariates in the model (age and BMI- both continuous variables) whereas the dependent variable is Outcome(Yes or No) and independent variable is Group (1 or 2).

fit<-glm(Outcome~Group, data=data.1, family=binomial(link="log"))

and it works fine.

When I try putting age in the model, it still works fine. However, when I put BMI in the model, it gives me the following:

Error: no valid set of coefficients has been found: please supply starting values

I have been tried different combination of starting values such as:

fit<-glm(Outcome~Group+Age+BMI, data=data.1, family=binomial(link="log"), start=c(0,0,0,0) or even start=(1,4) or start =4 but it still gives me the error.

It also says:

Error in glm.fit(x = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  : 
  length of 'start' should equal 4 and correspond to initial coefs for c("(Intercept)", "group1", "age", "bmi")

Any help on this will be much appreciated!

Edited: adding reproducible example.

N=50
data.1=data.frame(Outcome=sample(c(0,0,1),N, rep=T),Age=runif(N,8,58),BMI=rnorm(N,25,6),
                  Group=rep(c(0,1),length.out=N))
data.1$Group<-as.factor(data.1$Group)
fit<-glm(Outcome~Group, data=data.1, family=binomial(link="log"))
coefini=coef(glm(Outcome~Group+Age+BMI, data=data.1,family =binomial(link = "logit") ))
fit<-glm(Outcome~Group+Age+BMI, data=data.1, family=binomial(link="log"),start=coefini)

After some trial and error, using set.seed(123):

coefini=coef(glm(Outcome~Group+Age, data=data.1,family =binomial(link = "log") ))
fit2<-glm(Outcome~Group+Age+BMI, data=data.1, family=binomial(link="log"),start=c(coefini,0))

summary(fit2)

Call:
glm(formula = Outcome ~ Group + Age + BMI, family = binomial(link = "log"), 
    data = data.1, start = c(coefini, 0))

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.2457  -0.9699  -0.7725   1.2737   1.6799  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.5816964  1.0616813  -1.490    0.136
Group1       0.4987848  0.3958399   1.260    0.208
Age          0.0091428  0.0138985   0.658    0.511
BMI         -0.0005498  0.0331120  -0.017    0.987

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 65.342  on 49  degrees of freedom
Residual deviance: 63.456  on 46  degrees of freedom
AIC: 71.456

Number of Fisher Scoring iterations: 3