Why It Is Worth Going First
A pangram uses all seven letters and pays a seven point bonus on top of its length, so a seven letter pangram is worth fourteen where an ordinary seven letter word is worth seven. Finding one early is worth more than several minutes of grinding out four letter words, and it also tells you which letter combinations the puzzle likes.
Start From The Rare Letter
Look at the seven letters and find the one that appears in fewest words. Across the whole corpus the rarest letters are W at 7 percent, Z at 4 percent, X at 3 percent, Q at 2 percent, J at 1 percent. If the puzzle contains one of those, the pangram almost certainly uses it in an obvious place, usually a common prefix or suffix, because there are not many other options. That constraint cuts the search down faster than working from the common letters.
Then Check The Endings
Most pangrams are an ordinary word with an ordinary ending, not an exotic one. Try the centre letter combined with -ING, -ED, -ER, -ABLE and -TION before you try anything clever. If the letters allow a double letter, try that too, because the puzzle is allowed to reuse letters and people forget.
Or Just Look
The Spelling Bee Solver takes the centre letter and the six around it and lists every word in the 268,446 word pool that fits, with the pangrams separated out at the top.
More like this in the guides index, or put your own letters into the Word Unscrambler.