Depends on how lucky you get from enchanting
I usually hit level 30 by the time I find the first diamonds, at which point I plop down an enchantment table and enchant a diamond pick (if I have the leather for the books, that is). And since I play with hard mode recipes for TE, that means I usually have my first lvl 30 enchanted tool before I even build a pulverizer. I have not yet gotten a silk touch pick out of that first enchant... but then again I've only started two worlds in the past three months. I'm sure some others will get it on the first try
Besides, as you stated there are alternatives.