It is not possible to get that output in simple numeric form. The result depends upon the unresolved variables l, p and q.
About the best you can do is produce an output under each of the two possible conditions implied by your use of min()
syms n m p q s l up_lt
Q = @(v) sym(v);
mu = Q(1.0051);
nu = Q(0.1015);
eta = Q(0.0922);
k=2;
x1 = 2.*q + l - m;
y1 = 2.*p - n;
up_lt_vals = [x1, y1];
up_lt_cond = [x1 <= y1, y1 <= x1];
n_up_lt = length(up_lt_vals);
outp = zeros(n_up_lt, 1, 'sym');
outm = zeros(n_up_lt, 1, 'sym');
for up_lt_idx = 1 : n_up_lt
assume([n, m, p, q, s, l, up_lt], 'clear')
assumeAlso(p>=0);
assumeAlso(q>=0);
assumeAlso(l>=0);
assumeAlso(s>=0);
assumeAlso(m>=0);
assumeAlso(n>=0);
assumeAlso(up_lt_cond(up_lt_idx));
up_lt = up_lt_vals(up_lt_idx); %%%%%%%%% Upper limit of the sum in sGnmp3
Gnmp1 = (((-1).^(k-l))-1).*nchoosek(k,l).*((eta.*(mu-nu)).^(k-l)).*((mu.*nu./2).^l);
sGnmp1 = symsum(Gnmp1,l,0,k);
Gnmp2 = (1./(factorial(p).*factorial(q))).*nchoosek(p,n-p).*nchoosek(q,m-q);
sGnmp2 = symsum(symsum(Gnmp2,q,0,m),p,0,n);
Gnmp3 = ((2.*mu./nu).^s).*factorial(s).*nchoosek(x1,s) .*nchoosek(y1,s).*hermiteH(x1-s,0).*hermiteH(y1-s, 0);
sGnmp3 = symsum(Gnmp3,s,0,up_lt);
Gnmm1 = (((-1).^(k-l))+1).*nchoosek(k,l).*((eta.*(mu-nu)).^(k-l)).*((mu.*nu./2).^l);
sGnmm1 = symsum(Gnmm1,l,0,k);
Gnmp = symfun((sqrt(factorial(n).*factorial(m)).*((nu./(2.*mu)).^((n+m)./2)).*sGnmp1.*sGnmp2.*sGnmp3),[n,m]);
Gnmm = symfun((sqrt(factorial(n).*factorial(m)).*((nu./(2.*mu)).^((n+m)./2)).*sGnmm1.*sGnmp2.*sGnmp3),[n,m]);
outp(up_lt_idx) = simplify(Gnmp(6,5), 'steps', 5); %%% n and m can be taken as any positive integer.
outm(up_lt_idx) = simplify(Gnmm(5,5), 'steps', 5);
end
disp(up_lt_cond(1));
disp([outp(1); outm(1)]);
disp(up_lt_cond(2));
disp([outp(2); outm(2)]);
but this will not be very different than your existing code with min(). If more information was known about p, q, or l, then perhaps there might be additional simplification.
